Critical points approaches to elliptic problems driven by a p(x)-Laplacian

We establish the existence of at least three solutions for elliptic problems driven by a p(x)-Laplacian. The existence of at least one nontrivial solution is also proved. The approaches are based on the variational methods and critical-point theory.Встановлено існування принаймні трьох розв'язків еліптичних задач з p(x)-лапласіаном. Існування щонайменше одного нетривіального розв'язку також продемонстровано. Застосовані підходи ґрунтуються на варіаційних методах та теорії критичних точок

Perturbed nonlocal fourth order equations of Kirchhoff type with Navier boundary conditions

Abstract We investigate the existence of multiple solutions for perturbed nonlocal fourth-order equations of Kirchhoff type under Navier boundary conditions. We give some new criteria for guaranteeing that the perturbed fourth-order equations of Kirchhoff type have at least three weak solutions by using a variational method and some critical point theorems due to Ricceri. We extend and improve some recent results. Finally, by presenting two examples, we ensure the applicability of our results

Multiple solutions for a class of perturbed second-order differential equations with impulses

n/

Existence of three anti-periodic solutions for second-order impulsive differential inclusions with two parameters

Applying two three critical points theorems, we prove the existence of at least three anti-periodic solutions for a second-order impulsive differential inclusion with a perturbed nonlinearity and two parameters

On the Existence of Three Solutions for a Dirichlet Boundary Value Problem in N-dimensional Case

Abstract: In this note, we establish the existence of three weak solutions to the Dirichlet boundary value problem where is non-empty bounded open set with smooth boundary ∂Ω , p > N, λ > 0 and f : R → R is a continuous function. The result is based on a recent three critical points theorem

Multiple solutions for a perturbed mixed boundary value problem involving the one-dimensional p-Laplacian

The existence of three distinct weak solutions for a perturbed mixed boundary value problem involving the one-dimensional p-Laplacian operator is established under suitable assumptions on the nonlinear term. Our approach is based on recent variational methods for smooth functionals defined on reflexive Banach spaces