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On Neumann boundary value problems for elliptic equations

100%

Kandilakis D.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2004

tom 24

nr 1

31-40

We provide two existence results for the nonlinear Neumann problem ⎧-div(a(x)∇u(x)) = f(x,u) in Ω ⎨ ⎩∂u/∂n = 0 on ∂Ω, where Ω is a smooth bounded domain in $ℝ^N$, a is a weight function and f a nonlinear perturbation. Our approach is variational in character.

A generalization of the saddle point method with applications

100%

Schechter M.

Annales Polonici Mathematici

1992

tom 57

nr 3

269-281

We show that one can drop an important hypothesis of the saddle point theorem without affecting the result. We then show how this leads to stronger results in applications.

Existence of a nontrival solution for Dirichlet problem involving p(x)-Laplacian

88%

Barnaś S.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2014

tom 34

nr 1

15-39

In this paper we study the nonlinear Dirichlet problem involving p(x)-Laplacian (hemivariational inequality) with nonsmooth potential. By using nonsmooth critical point theory for locally Lipschitz functionals due to Chang [6] and the properties of variational Sobolev spaces, we establish conditions which ensure the existence of solution for our problem.

Ograniczanie wyników

2 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Annales Polonici Mathematici

1 Barnaś S.

1 Kandilakis D.

1 Schechter M.

1 2014

1 2004

1 1992

Wyniki wyszukiwania

On Neumann boundary value problems for elliptic equations

A generalization of the saddle point method with applications

Existence of a nontrival solution for Dirichlet problem involving p(x)-Laplacian