Nontrivial solutions for a nonlinear Schrodinger equation with nonsymmetric coefficients

This paper is dedicated to studying the nonlinear Schrodinger equations of the form {-Delta u+lambda u = a(x)f(u), x is an element of R-N ; u is an element of H-1 (R-N), where a is an element of C-1( R-N, [0, infinity)) is nonsymmetric and satisfies a(x) <= (not equivalent to) a(infinity) := lim(vertical bar y vertical bar ->infinity) a(y), and f is an element of C(R, R). By using concentration compactness arguments and projections on a general Pohozaev type manifold, we prove that the above problem has a nontrivial solution under weaker assumptions on a and f than the existing results in literature. (C) 2020 Elsevier Ltd. All rights reserved.