Search results for "solution"

Multiple solutions for nonlinear nonhomogeneous resonant coercive problems

2018

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 …

Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces

2015

Submitted by Alexandre Almeida (jaralmeida@ua.pt) on 2015-11-12T11:41:07Z No. of bitstreams: 1 RieszWolff_RIA.pdf: 159825 bytes, checksum: d99abdf3c874f47195619a31ff5c12c7 (MD5) Approved for entry into archive by Bella Nolasco(bellanolasco@ua.pt) on 2015-11-17T12:18:41Z (GMT) No. of bitstreams: 1 RieszWolff_RIA.pdf: 159825 bytes, checksum: d99abdf3c874f47195619a31ff5c12c7 (MD5) Made available in DSpace on 2015-11-17T12:18:41Z (GMT). No. of bitstreams: 1 RieszWolff_RIA.pdf: 159825 bytes, checksum: d99abdf3c874f47195619a31ff5c12c7 (MD5) Previous issue date: 2015-04

Multiple solutions of second order Hamiltonian systems

2017

Author(s): Bonanno, G; Livrea, R; Schechter, M | Abstract: The existence and the multiplicity of periodic solutions for a parameter dependent second order Hamiltonian system are established via linking theorems. A monotonicity trick is adopted in order to prove the existence of an open interval of parameters for which the problem under consideration admits at least two non trivial qualified solutions.

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

2014

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.

Existence and multiplicity results for semilinear elliptic Dirichlet problems in exterior domains

1995

Solutions and positive solutions for superlinear Robin problems

2019

We consider nonlinear, nonhomogeneous Robin problems with a (p − 1)-superlinear reaction term, which need not satisfy the Ambrosetti-Rabinowitz condition. We look for positive solutions and prove existence and multiplicity theorems. For the particular case of the p-Laplacian, we prove existence results under a different geometry near the origin.We consider nonlinear, nonhomogeneous Robin problems with a (p − 1)-superlinear reaction term, which need not satisfy the Ambrosetti-Rabinowitz condition. We look for positive solutions and prove existence and multiplicity theorems. For the particular case of the p-Laplacian, we prove existence results under a different geometry near the origin.

A multiplicity theorem for parametric superlinear (p,q)-equations

2020

We consider a parametric nonlinear Robin problem driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (\((p,q)\)-equation). The reaction term is \((p-1)\)-superlinear but need not satisfy the Ambrosetti-Rabinowitz condition. Using variational tools, together with truncation and comparison techniques and critical groups, we show that for all small values of the parameter, the problem has at least five nontrivial smooth solutions, all with sign information.

Green’s function and existence of solutions for a third-order three-point boundary value problem

2019

The solutions of third-order three-point boundary value problem x‘‘‘ + f(t, x) = 0, t ∈ [a, b], x(a) = x‘(a) = 0, x(b) = kx(η), where η ∈ (a, b), k ∈ R, f ∈ C([a, b] × R, R) and f(t, 0) ≠ 0, are the subject of this investigation. In order to establish existence and uniqueness results for the solutions, attention is focused on applications of the corresponding Green’s function. As an application, also one example is given to illustrate the result. Keywords: Green’s function, nonlinear boundary value problems, three-point boundary conditions, existence and uniqueness of solutions.

In vitro antimicrobial activity of sodium hypochlorite, chlorhexidine gluconate and octenidine dihydrochloride in elimination of microor- ganisms wit…

2011

The aim of this study was to evaluate the effectiveness of different irrigation solutions at different time intervals for the elimination of E.faecalis and C.albicans penetrated into the dentine tubules of primary and permanent teeth in vitro. The 4 mm primary and permanent teeth sections were sterilized and contaminated with a mixture of E.faecalis and C.albicans strains. After the application of different irrigation solutions (Sodium hypochlorite, Chlorhexidine gluconate, Octenidine Dihydrochloride, saline) to the contaminated tooth sections according to study groups, neutralizers were applied for inactivation of the solutions after 30 sec, 1 min and 5 min. Dentine shavings were placed in…

Existence of a unique solution for a third-order boundary value problem with nonlocal conditions of integral type

2021

The existence of a unique solution for a third-order boundary value problem with integral condition is proved in several ways. The main tools in the proofs are the Banach fixed point theorem and the Rus’s fixed point theorem. To compare the applicability of the obtained results, some examples are considered.