Linear elliptic system with nonlinear boundary conditions without Landesman-Lazer conditions

Abstract

The boundary value problem is examined for the system of elliptic equations of from $-\Delta u+A(x)u=0\text{in}\Omega ,$ where $A(x)$ is positive semidefinite matrix on ${\mathbb{R}}^{k\times k},$ and $\frac{\partial u}{\partial \nu }+g(u)=h(x)\text{on}\partial \Omega$ It is assumed that $g\in C({\mathbb{R}}^k,{\mathbb{R}}^k)$ is a bounded function which may vanish at infinity. The proofs are based on Leray-Schauder degree methods.

References in corpus (1)

• Linear second order elliptic partial differential equations with nonlinear boundary conditions at resonance without landesman-lazer conditions