Existence of infinitely solutions for a modified nonlinear Schrodinger equation via dual approach

Abstract

<p>In this article, we focus on the existence of infinitely many weak solutions for the modified nonlinear Schrödinger equation</p> <pre>-∆u + V(x)u - [∆(1 + u²)^α/2] αu/2(1 + u²)^2-α/2 = ƒ(x, u), in ℝ^N,</pre> <p>where 1 ≤ α < 2, ƒ ∈ C(ℝ^N x ℝ, ℝ). By using a symmetric mountain pass theorem and dual approach, we prove that the above equation has infinitely many high energy solutions.</p>