Multiple solutions for p-Laplacian type problems with asymptotically p-linear terms via a cohomological index theory

Nontrivial Solutions of p-Superlinear p-Laplacian Problems via a Cohomological Local Splitting

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.

Existence of Periodic Solutions for a Class of Asymptotically p-Linear Discrete Systems Involving p-Laplacian

Multiple solutions for p(x)-Laplacian type equations

We prove the existence of at least three weak solutions for the Dirichlet problem when the nonlinear term f is sublinear and p(x) is greater than n. This Dirichlet problem involves a general elliptic operator in divergence form (in particular, a p(x)-Laplace operator). Our method relies upon a recent critical point theorem obtained by Bonanno and Marano, and is combined with the theory of varia...

Existence of Homoclinic Orbits for a Class of Asymptotically p-Linear Difference Systems with p-Laplacian

and Applied Analysis 3 W4 W̃ n, x ∇W n, x , x − pW n, x , lim |x|→∞ W̃ n, x ∞ uniformly for n ∈ Z, 1.7 and for any fixed 0 < c1 < c2 < ∞, inf n∈Z, c1≤|x|≤c2 W̃ n, x |x| > 0. 1.8 Then problem 1.1 has at least one nontrivial homoclinic solution. Remark 1.2. The function W n, x in this paper is asymptotically p-linear at infinity. The behavior of the gradient of W n, x at infinity is like that of a f...

MULTIPLICITY RESULTS FOR p-SUBLINEAR p-LAPLACIAN PROBLEMS INVOLVING INDEFINITE EIGENVALUE PROBLEMS VIA MORSE THEORY

We establish some multiplicity results for a class of p-sublinear pLaplacian problems involving indefinite eigenvalue problems using Morse theory.