Ground state solution for a non-autonomous 1-Laplacian problem involving periodic potential in RN

摘要

In this paper, we consider the following 1-Laplacian problem @@@ -Delta(1)u+V(x)u/vertical bar u vertical bar = f(x,u), x is an element of R-N, u>0, u is an element of BV(R-N), @@@ where Delta(1)u = div(Du vertical bar Du vertical bar), V is a periodic potential and f is periodic and verifies the super-primary condition at infinity. By the Nehari type manifold method, the concentration compactness principle and some analysis techniques, we show the 1-Laplacian equation has a ground state solution.

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