On the existence and multiplicity of solutions for Dirichlet's problem for fractional differential equations

In this paper, by using variational methods and critical point theorems, we prove the existence and multiplicity of solutions for boundary value problem for fractional order differential equations where Riemann-Liouville fractional derivatives and Caputo fractional derivatives are used. Our results extend the second order boundary value problem to the non integer case. Moreover, some conditions to determinate nonnegative solutions are presented and examples are given to illustrate our results.

On a stochastic SIR model

We consider a stochastic SIR system and we prove the existence, uniqueness and positivity of solution. Moreover the existence of an invariant measure under a suitable condition on the coefficients is studied.

Modello stocastico di epidemia

On a mixed boundary value problem involving the p-Laplacian

In this paper we prove the existence of infinitely many solutions for a mixed boundary value problem involving the one dimensional p-Laplacian. A result on the existence of three solutions is also established. The approach is based on multiple critical points theorems.

Multiple solutions for nonlinear nonhomogeneous resonant coercive problems

We consider a nonlinear, nonhomogeneous Dirichlet problem driven by the sum of a \begin{document}$p$\end{document} -Laplacian ( \begin{document}$2 ) and a Laplacian. The reaction term is a Caratheodory function \begin{document}$f(z,x)$\end{document} which is resonant with respect to the principal eigenvalue of ( \begin{document}$-\Delta_p,\, W^{1,p}_0(\Omega)$\end{document} ). Using variational methods combined with truncation and comparison techniques and Morse theory (critical groups) we prove the existence of three nontrivial smooth solutions all with sign information and under three different conditions concerning the behavior of \begin{document}$f(z,\cdot)$\end{document} near zero. By …

Multiple solutions for a Sturm-Liouville problem with mixed boundary conditions

Approximation of fixed points of asymptotically g-nonexpansive mapping

EXISTENCE OF THREE SOLUTIONS FOR A MIXED BOUNDARY VALUE PROBLEM WITH THE STURM-LIOUVILLE EQUATION

Abstract. The aim of this paper is to establish the existence of threesolutions for a Sturm-Liouville mixed boundary value problem. The ap-proach is based on multiple critical points theorems. 1. IntroductionThe aim of this paper is to establish, under a suitable set of assumptions, theexistence of at least three solutions for the following Sturm-Liouville problemwith mixed boundary conditions(RS λ )ˆ−(pu ′ ) ′ +qu = λf(t,u) in I =]a,b[u(a) = u ′ (b) = 0,where λ is a positive parameter and p, q, f are regular functions. To be precise,if f : [a,b] × R→ Ris a L 2 -Carath´eodory function and p,q ∈ L ∞ ([a,b]) suchthatp 0 := essinf t∈[a,b] p(t) > 0, q 0 := essinf t∈[a,b] q(t) ≥ 0,then we prove …

Existence and multiplicity of solutions for non linear elliptic Dirichlet systems

The existence and multiplicity of solutions for systems of nonlinear elliptic equations with Dirichlet boundary conditions is investigated. Under suitable assumptions on the potential of the nonlinearity, the existence of one, or two, or three solutions is established. Our approach is based on variational methods.

SIVS epidemic model with stochastic perturbation

Multi-Phase epidemic model by a Markov chain

Abstract In this paper we propose a continuous-time Markov chain to describe the spread of an infective and non-mortal disease into a community numerically limited and subjected to an external infection. We make a numerical simulation that shows tendencies for recurring epidemic outbreaks and for fade-out or extinction of the infection.

Multiple solutions for a mixed boundary value problem

Parasite population delay model of malaria type with stochastic perturbation and environmental criterion for limitation of disease

AbstractWe present a stochastic delay model of an infectious disease (malaria) transmitted by a vectors (mosquitoes) after an incubation time. A criterion for limitation of disease is found.

Location of solutions for quasi-linear elliptic equations with general gradient dependence

Existence and location of solutions to a Dirichlet problem driven by $(p,q)$-Laplacian and containing a (convection) term fully depending on the solution and its gradient are established through the method of subsolution-supersolution. Here we substantially improve the growth condition used in preceding works. The abstract theorem is applied to get a new result for existence of positive solutions with a priori estimates.

Equilibrium in a duopoly game with homogeneous adaptive expectations and isoelastic demand

In this paper we consider a non linear discrete time Cournot duopoly game with isoelastic demand and where players have homogeneous adaptive expectations. The evolution of expected outputs over time is generated by the iteration of two-dimensional map and the long-run behavior is characterized by equilibrium points which are locally stable.

Equazioni monodimensionali di un gas viscoso barotropico con una perturbazione poco regolare

Si considerino le equazioni di un gas viscoso barotropico in una dimensione spazialedν=(μ(ϱνe)e−pe)dt+dG,ϱt+ϱ2νe=0,p=ϱγ con una perturbazionedG sotto l’ipotesi cheG sia una funzione a variazione limitata inL2(Θ) o inH01 (Θ) (Θ=]0, α[) e si dimostrano l’esistenza e l’unicita della soluzione globale in una classe di soluzioni di «tipo forte» ed in una di «tipo debole». Questo risultato costituisce una generalizzazione del risultato di Kazhikhov [8] e di Shelukhin [10] e contiene osservazioni preliminari per le corrispondenti equazioni stocastiche.

A note on the existence of an invariant measure for a stochastic model with periodic coefficients

We consider a stochastic model of malaria which concern the infected population and the vector population and whose coefficients are periodic functions. Under a suitable condition the existence of an invariant measure is proved.

Esistenza e molteplicità di soluzioni per problemi differenziali non lineari con condizioni miste

Bounded weak solutions to superlinear Dirichlet double phase problems

AbstractIn this paper we study a Dirichlet double phase problem with a parametric superlinear right-hand side that has subcritical growth. Under very general assumptions on the data, we prove the existence of at least two nontrivial bounded weak solutions to such problem by using variational methods and critical point theory. In contrast to other works we do not need to suppose the Ambrosetti–Rabinowitz condition.

Two positive solutions for a Dirichlet problem with the (p,q)‐Laplacian

The aim of this paper is to prove the existence of two solutions for a nonlinear elliptic problem involving the (p,q) -Laplacian operator. The solutions are obtained by using variational methods and critical points theorems. The positivity of the solutions is shown by applying a generalized version of the strong maximum principle.

Stability of a stochastic SIR system

Stability of a stochastic SIR system

Abstract We propose a stochastic SIR model with or without distributed time delay and we study the stability of disease-free equilibrium. The numerical simulation of the stochastic SIR model shows that the introduction of noise modifies the threshold of system for an epidemic to occur and the threshold stochastic value is found.

Elliptic problems with convection terms in Orlicz spaces

Abstract The existence of a solution to a Dirichlet problem, for a class of nonlinear elliptic equations, with a convection term, is established. The main novelties of the paper stand on general growth conditions on the gradient variable, and on minimal assumptions on Ω. The approach is based on the method of sub and supersolutions. The solution is a zero of an auxiliary pseudomonotone operator build via truncation techniques. We present also some examples in which we highlight the generality of our growth conditions.

A sub-supersolution approach for Neumann boundary value problems with gradient dependence

Abstract Existence and location of solutions to a Neumann problem driven by an nonhomogeneous differential operator and with gradient dependence are established developing a non-variational approach based on an adequate method of sub-supersolution. The abstract theorem is applied to prove the existence of finitely many positive solutions or even infinitely many positive solutions for a class of Neumann problems.

On a stochastic disease model with vaccination

We propose a stochastic disease model where vaccination is included and such that the immunity isn’t permanent. The existence, uniqueness and positivity of the solution and the stability of disease free equilibrium is studied. The numerical simulation is done.

Ordinary (p_1,...,p_m)-Laplacian system with mixed boundary value

In this paper we prove the existence of multiple weak solutions for an ordinary mixed boundary value system with (p_1,...,p_m)-Laplacian by using recent results of critical points.

Quasilinear Dirichlet Problems with Degenerated p-Laplacian and Convection Term

The paper develops a sub-supersolution approach for quasilinear elliptic equations driven by degenerated p-Laplacian and containing a convection term. The presence of the degenerated operator forces a substantial change to the functional setting of previous works. The existence and location of solutions through a sub-supersolution is established. The abstract result is applied to find nontrivial, nonnegative and bounded solutions.

Existence and asymptotic properties for quasilinear elliptic equations with gradient dependence

Abstract The paper focuses on a Dirichlet problem driven by the ( p , q ) -Laplacian containing a parameter μ > 0 in the principal part of the elliptic equation and a (convection) term fully depending on the solution and its gradient. Existence of solutions, uniqueness, a priori estimates, and asymptotic properties as μ → 0 and μ → ∞ are established under suitable conditions.

Three weak solutions for elliptic Dirichlet system

Simple epidemic model by a Markov chain

In this paper we propose a continuous-time Markov chain to describe a SIs model with and without external reinfection

Multi-phase epidemic model and its numerical simulation

Stochastic equation of population dynamics with diffusion on a domain

We consider Lotka-Volterra competition model with diffusion in a territorial domain with a stochastic perturbation which represents the random variations of environment conditions. We prove the existence, the uniqueness and the positivity of the solution. Moreover, the stochastic boundedness of the solution is analized.

Multiple solutions for a Sturm-Liouville problem with periodic boundary conditions

The main purpose of this paper is to establish the existence of multiple solutions for a Sturm-Liouville problem with periodic boundary conditions. The approach is based on variational methods and multiple critical points theorems

A note on stochastic model of malaria with periodic coefficients

Mesure invariante d'une equation integrale stochastique a coefficients periodiques et applications a un modele d'epidemiologie

We consider a stochastic integral equation, whose coe cients are periodic in time. Under a suitable condition we prove the existence of an invariant mesure for this stochastic equation. This invariant mesure is constructed on a Banach space of continuous functions. We study also its application to an epidemiologic model of malaria, which concerns the infected population and the vector population.

Positive solutions for the Neumann p-Laplacian

We examine parametric nonlinear Neumann problems driven by the p-Laplacian with asymptotically ( $$p-1$$ )-linear reaction term f(z, x) (as $$x\rightarrow +\infty $$ ). We determine the existence, nonexistence and minimality of positive solutions as the parameter $$\lambda >0$$ varies.

Infinitely many solutions to boundary value problem for fractional differential equations

Variational methods and critical point theorems are used to discuss existence of infinitely many solutions to boundary value problem for fractional order differential equations where Riemann-Liouville fractional derivatives and Caputo fractional derivatives are used. An example is given to illustrate our result.

Two Nontrivial Solutions for Robin Problems Driven by a p–Laplacian Operator

By variational methods and critical point theorems, we show the existence of two nontrivial solutions for a nonlinear elliptic problem under Robin condition and when the nonlinearty satisfies the usual Ambrosetti-Rabinowitz condition.

Regular solutions for nonlinear elliptic equations, with convective terms, in Orlicz spaces

We establish some existence and regularity results to the Dirichlet problem, for a class of quasilinear elliptic equations involving a partial differential operator, depending on the gradient of the solution. Our results are formulated in the Orlicz-Sobolev spaces and under general growth conditions on the convection term. The sub- and supersolutions method is a key tool in the proof of the existence results.

Two non-zero solutions for Sturm–Liouville equations with mixed boundary conditions

Abstract In this paper, we establish the existence of two non-zero solutions for a mixed boundary value problem with the Sturm–Liouville equation. The approach is based on a recent two critical point theorem.

Ordinary (p1,…,pm)-Laplacian systems with mixed boundary value conditions

Abstract In this paper we prove the existence of multiple weak solutions for an ordinary mixed boundary value system with ( p 1 , … , p m )-Laplacian by using recent results of critical points.

Existence of three solutions for a mixed boundary value system with (p_1,...,p_m)-Laplacian

In this paper we prove the existence of at least three weak solutions for a mixed boundary value system with (p_1,,...,p_m)-Laplacian. The approach is based on variational methods.

SIRV epidemic model with stochastic perturbation

We propose a stochastic disease model where vaccination is included and such that the immunity is permanent. The existence, uniqueness and positivity of the solution and the stability of the disease free-equilibrium are studied

Multiple Solutions for Fractional Boundary Value Problems

Variational methods and critical point theorems are used to discuss existence and multiplicity of solutions for fractional boundary value problem where Riemann–Liouville fractional derivatives and Caputo fractional derivatives are used. Some conditions to determinate nonnegative solutions are presented. An example is given to illustrate our results.

A Sub-Supersolution Approach for Robin Boundary Value Problems with Full Gradient Dependence

The paper investigates a nonlinear elliptic problem with a Robin boundary condition, which exhibits a convection term with full dependence on the solution and its gradient. A sub- supersolution approach is developed for this type of problems. The main result establishes the existence of a solution enclosed in the ordered interval formed by a sub-supersolution. The result is applied to find positive solutions.

Infinitely many weak solutions for a mixed boundary value system with (p_1,…,p_m)-Laplacian

The aim of this paper is to prove the existence of infinitely many weak solu- tions for a mixed boundary value system with (p1, . . . , pm)-Laplacian. The approach is based on variational methods.

Positive solutions for nonlinear Robin problems with convection

We consider a nonlinear Robin problem driven by the p-Laplacian and with a convection term f(z,x,y). Without imposing any global growth condition on f(z,·,·) and using topological methods (the Leray-Schauder alternative principle), we show the existence of a positive smooth solution.

Infinitely many solutions for a mixed boundary value problem

The existence of infinitely many solutions for a mixed boundary value problem is established. The approach is based on variational methods.