Multiplicity and concentration results for a (p, q)-Laplacian problem in $${\mathbb {R}}^{N}$$

Sign-changing solution and ground state solution for a class of (p,q)$(p,q)$-Laplacian equations with nonlocal terms on RN$\mathbb{R}^{N}$

In the paper, we investigate the least energy sign-changing solution and the ground state solution of a class of (p,q)-Laplacian equations with nonlocal terms on RN . Applying the constraint variational method, the quantitative deformation lemma, and topological degree theory, we see that the equation has one least energy sign-changing solution u. Moreover, we regard c, d as parameters and give...

Multiplicity results of a Neumann Problem for p(x)-Laplacian Systems

In this paper, we study a Neumann problem for elliptic systems with variable exponents and we obtain the existence of at least three nontrivial solutions by using an equivalent variational approach to a recent Ricceri’s three critical points theorem [12].

Nonexistence and existence results for a 2$n$th-order $p$-Laplacian discrete Neumann boundary value problem

This paper is concerned with a 2nth-order p-Laplacian difference equation. By using the critical point method, we establish various sets of sufficient conditions for the nonexistence and existence of solutions for Neumann boundary value problem and give some new results. Results obtained successfully generalize and complement the existing ones.

EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A DIFFERENTIAL INCLUSION PROBLEM INVOLVING THE p(x)-LAPLACIAN

In this article we consider the differential inclusion − div(|∇u|p(x)−2∇u) ∈ ∂F (x, u) in Ω, u = 0 on ∂Ω which involves the p(x)-Laplacian. By applying the nonsmooth Mountain Pass Theorem, we obtain at least one nontrivial solution; and by applying the symmetric Mountain Pass Theorem, we obtain k-pairs of nontrivial solutions in W 1,p(x) 0 (Ω).

Solutions for singular p-Laplacian equation in Rn