On Neumann boundary value problems for elliptic equations

Dimitrios Kandilakis

ArticleOriginal scientific text

Title

On Neumann boundary value problems for elliptic equations

Authors ¹

Affiliations

Department of Sciences, Technical University of Crete, Chania, Crete 73100, Greece

Abstract

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.

Keywords

ENG

variational methods, Palais-Smale condition, saddle point theorem, mountain pass theorem

D. Arcoya and L. Orsina, Landesman-Laser conditions and quasilinear elliptic equations, Nonlin. Anal. TMA 28 (1997), 1623-1632.
J. Bouchala and P. Drabek, Strong resonance for some quasilinear elliptic equations, J. Math. Anal. Appl. 245 (2000), 7-19.
P. Caldiroli and R. Musina, On a variational degenerate elliptic problem, NoDEA 7 (2000), 187-199.
F. Cîrstea, D. Motreanu and V. Radulescu, Weak solutions of quasilinear problems with nonlinear boundary condition, Nonlin. Anal. 43 (2001), 623-636.
P. Drabek, A. Kufner and F. Nicolosi, Quasilinear Elliptic Equations with Degenerations and Singulaties, W. De Gruyter 1997.
W. Li and H. Zhen, The applications of sums of ranges of accretive operators to nonlinear equations involving the p-Laplacian operator, Nonlin. Anal. TMA 24 (2) (1995), 185-193.
P.H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, Amer. Math. Soc. Prividence, 1976.

Title

On Neumann boundary value problems for elliptic equations

Affiliations

Abstract

Keywords

Bibliography