Nontrivial solutions for a nonlinear Schrödinger equation with nonsymmetric coefficients. (June 2020) - Wang, Xiaoping; Liao, Fangfang
Abstract: This paper is dedicated to studying the nonlinear Schrödinger equations of the form − △ u + λ u = a ( x ) f ( u ), x ∈ R N ; u ∈ H 1 ( R N ), where a ∈ C 1 ( R N, [ 0, ∞ ) ) is nonsymmetric and satisfies a ( x ) ≤ ( ⁄ ≡ ) a ∞ ≔ lim | y | → ∞ a ( y ), and f ∈ 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.