Search results for "Positive solution"
showing 10 items of 30 documents
Existence Results for Periodic Boundary Value Problems with a Convenction Term
2020
By using an abstract coincidence point theorem for sequentially weakly continuous maps the existence of at least one positive solution is obtained for a periodic second order boundary value problem with a reaction term involving the derivative \(u'\) of the solution u: the so called convention term. As a consequence of the main result also the existence of at least one positive solution is obtained for a parameter-depending problem.
Asymptotic behavior of positive solutions of a Dirichlet problem involving supercritical nonlinearities
2013
On a Robin (p,q)-equation with a logistic reaction
2019
We consider a nonlinear nonhomogeneous Robin equation driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (\((p,q)\)-equation) plus an indefinite potential term and a parametric reaction of logistic type (superdiffusive case). We prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter \(\lambda \gt 0\) varies. Also, we show that for every admissible parameter \(\lambda \gt 0\), the problem admits a smallest positive solution.
Two positive solutions for a nonlinear parameter-depending algebraic system
2021
The existence of two positive solutions for a nonlinear parameter-depending algebraic system is investigated. The main tools are a finite dimensional version of a two critical point theorem and a recent weak-strong discrete maximum principle.
Oscillation of Second-Order Neutral Differential Equations
2013
Author's version of an article in the journal: Funkcialaj Ekvacioj. Also available from the publisher at: http://www.math.kobe-u.ac.jp/~fe/ We study oscillatory behavior of a class of second-order neutral differential equations relating oscillation of these equations to existence of positive solutions to associated first-order functional differential inequalities. Our assumptions allow applications to differential equations with both delayed and advanced arguments, and not only. New theorems complement and improve a number of results reported in the literature. Two illustrative examples are provided.
Two positive solutions for a nonlinear parameter-depending algebraic system
2021
The existence of two positive solutions for a nonlinear parameter-depending algebraic system is investigated. The main tools are a finite dimensional version of a two critical point theorem and a recent weak-strong discrete maximum principle.
A Sub-Supersolution Approach for Robin Boundary Value Problems with Full Gradient Dependence
2020
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.
On the Sub-Supersolution Approach for Dirichlet Problems driven by a (p(x), q(x))-Laplacian Operator with Convection Term
2021
The method of sub and super-solution is applied to obtain existence and location of solutions to a quasilinear elliptic problem with variable exponent and Dirichlet boundary conditions involving a nonlinear term f depending on solution and on its gradient. Under a suitable growth condition on the convection term f, the existence of at least one solution satisfying a priori estimate is obtained.
Location of solutions for quasi-linear elliptic equations with general gradient dependence
2017
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.
Positive solutions for nonlinear Robin problems
2017
We consider a parametric Robin problem driven by the p-Laplacian with an indefinite potential and with a superlinear reaction term which does not satisfy the Ambrosetti-Rabinowitz condition. We look for positive solutions. We prove a bifurcation-type theorem describing the nonexistence, existence and multiplicity of positive solutions as the parameter varies. We also show the existence of a minimal positive solution $\tilde{u}_\lambda$ and establish the monotonicity and continuity of the map $\lambda\to \tilde{u}_\lambda$.