Nontrivial Solutions of p-Superlinear p-Laplacian Problems via a Cohomological Local Splitting
نویسنده
چکیده
We consider a quasilinear equation, involving the p-Laplace operator, with a p-superlinear nonlinearity. We prove the existence of a nontrivial solution, also when there is no mountain pass geometry, without imposing a global sign condition. Techniques of Morse theory are employed.
منابع مشابه
NONTRIVIAL CRITICAL GROUPS IN p -LAPLACIAN PROBLEMS VIA THE YANG INDEX
We construct and variationally characterize by a min-max procedure involving the Yang index a new sequence of eigenvalues of the pLaplacian, and use the structure provided by this sequence to show that the associated variational functional always has a nontrivial critical group. As an application we obtain nontrivial solutions for a class of p-superlinear problems.
متن کاملExistence of at least one nontrivial solution for a class of problems involving both p(x)-Laplacian and p(x)-Biharmonic
We investigate the existence of a weak nontrivial solution for the following problem. Our analysis is generally bathed on discussions of variational based on the Mountain Pass theorem and some recent theories one the generalized Lebesgue-Sobolev space. This paper guarantees the existence of at least one weak nontrivial solution for our problem. More precisely, by applying Ambrosetti and Rabinow...
متن کاملExistence and multiplicity of nontrivial solutions for $p$-Laplacian system with nonlinearities of concave-convex type and sign-changing weight functions
This paper is concerned with the existence of multiple positive solutions for a quasilinear elliptic system involving concave-convex nonlinearities and sign-changing weight functions. With the help of the Nehari manifold and Palais-Smale condition, we prove that the system has at least two nontrivial positive solutions, when the pair of parameters $(lambda,mu)$ belongs to a c...
متن کاملPositive solution for Dirichlet $p(t)$-Laplacian BVPs
In this paper we provide existence results for positive solution to Dirichlet p(t)-Laplacian boundary value problems. The sublinear and superlinear cases are considerd.
متن کاملInfinitely Many Homoclinic Solutions for Second Order Nonlinear Difference Equations with p-Laplacian
We employ Nehari manifold methods and critical point theory to study the existence of nontrivial homoclinic solutions of discrete p-Laplacian equations with a coercive weight function and superlinear nonlinearity. Without assuming the classical Ambrosetti-Rabinowitz condition and without any periodicity assumptions, we prove the existence and multiplicity results of the equations.
متن کامل