Search results for "Positive solution"

A singular (p,q)-equation with convection and a locally defined perturbation

2021

We consider a parametric Dirichlet problem driven by the (p,q)-Laplacian and a reaction which is gradient dependent (convection) and the competing effects of two more terms, one a parametric singular term and a locally defined perturbation. We show that for all small values of the parameter the problem has a positive smooth solution.

An existence result for a Neumann problem

2015

The main result of this paper deals with the existence of at least one positive solution for a second order Neumann boundary value problem. Such a result is obtained by using an abstract coincidence point theorem that allows to get our conclusion under non standard conditions on the nonlinearity.

Bifurcation phenomena for the positive solutions of semilinear elliptic problems with mixed boundary conditions

2016

We consider a parametric semilinear elliptic equation with a Cara-theodory reaction which exhibits competing nonlinearities. It is "concave" (sub-linear) near the origin and "convex" (superlinear) or linear near $+\infty$. Using variational methods based on the critical point theory, coupled with suitable truncation and comparison techniques, we prove a bifurcation-type theorem, describing the set of positive solutions as the parameter varies.

Parameter dependence for the positive solutions of nonlinear, nonhomogeneous Robin problems

2020

We consider a parametric nonlinear Robin problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential. The reaction term is $$(p-1)$$-superlinear but need not satisfy the usual Ambrosetti–Rabinowitz condition. We look for positive solutions and prove a bifurcation-type result for the set of positive solutions as the parameter $$\lambda >0$$ varies. Also we prove the existence of a minimal positive solution $$u_\lambda ^*$$ and determine the monotonicity and continuity properties of the map $$\lambda \rightarrow u_\lambda ^*$$.

A note on homoclinic solutions of (p,q)-Laplacian difference equations

2019

We prove the existence of at least two positive homoclinic solutions for a discrete boundary value problem of equations driven by the (p,q) -Laplace operator. The properties of the nonlinearity ensure that the energy functional, corresponding to the problem, satisfies a mountain pass geometry and a Palais–Smale compactness condition.

Positive solutions for the Neumann p-Laplacian

2017

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.

Perturbed eigenvalue problems for the Robin p-Laplacian plus an indefinite potential

2020

AbstractWe consider a parametric nonlinear Robin problem driven by the negativep-Laplacian plus an indefinite potential. The equation can be thought as a perturbation of the usual eigenvalue problem. We consider the case where the perturbation$$f(z,\cdot )$$f(z,·)is$$(p-1)$$(p-1)-sublinear and then the case where it is$$(p-1)$$(p-1)-superlinear but without satisfying the Ambrosetti–Rabinowitz condition. We establish existence and uniqueness or multiplicity of positive solutions for certain admissible range for the parameter$$\lambda \in {\mathbb {R}}$$λ∈Rwhich we specify exactly in terms of principal eigenvalue of the differential operator.

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.

Existence of two positive solutions for anisotropic nonlinear elliptic equations

2021

This paper deals with the existence of nontrivial solutions for a class of nonlinear elliptic equations driven by an anisotropic Laplacian operator. In particular, the existence of two nontrivial solutions is obtained, adapting a two critical point results to a suitable functional framework that involves the anisotropic Sobolev spaces.