Infinitely many solutions for quasilinear Schrödinger equation with general superlinear nonlinearity
Infinitely many solutions for quasilinear Schrödinger equation with general superlinear nonlinearity
Abstract In this article, we study the quasilinear Schrödinger equation $$ -\triangle (u)+V(x)u-\triangle \bigl(u^{2}\bigr)u=g(x,u), \quad x\in \mathbb{R}^{N}, $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>−</mml:mo> <mml:mi>△</mml:mi> <mml:mo>(</mml:mo> <mml:mi>u</mml:mi> <mml:mo>)</mml:mo> <mml:mo>+</mml:mo> <mml:mi>V</mml:mi> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>)</mml:mo> <mml:mi>u</mml:mi> <mml:mo>−</mml:mo> <mml:mi>△</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>u</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> <mml:mi>u</mml:mi> <mml:mo>=</mml:mo> <mml:mi>g</mml:mi> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:mi>u</mml:mi> <mml:mo>)</mml:mo> <mml:mo>,</mml:mo> …