Existence and nonexistence of solutions of asymptotically linear Klein-Gordon equation

Abstract

In this article we study a nonlinear Klein-Gordon equation when the nonlinear term asymptotically linear at infinity. We used the Pohozaev manifold to separate a subspace of $H^1(\mathbb{R}^N)$ on a global existence region and on a blow up region.

Keywords

• Klein-Gordon equation
• blow up of solution
• asymptotically linear
• Pohozaev manifold