A class of asymptotically periodic fractional Schrodinger equations with critical growth

作者：de Souza Manasses^*; Araujo Yane Lisley

来源：Communications in Contemporary Mathematics, 2018, 20(3): 1750011.

DOI：10.1142/S0219199717500110

• Variational methods
• critical growth
• fractional Schrodinger equation

In this paper, we study a class of fractional Schrodinger equations in RN of the form
(-Delta)(alpha) u + V(x)u = |u| (2*) alpha(-2)u + g(x,u),
where 0 < alpha < 1, 2 alpha < N, 2*(alpha) = 2N/(N - 2 alpha) is the critical Sobolev exponent, V : R-N -> R is a positive potential bounded away from zero, and the nonlinearity g : R-N x R -> R behaves like |u| (q- 2)u at infinity for some 2 < q < 2* (alpha), and does not satisfy the usual Ambrosetti- Rabinowitz condition. We also assume that the potential V (x) and the nonlinearity g(x, u) are asymptotically periodic at infinity. We prove the existence of at least one solution u is an element of H-alpha(R-N) by combining a version of the mountainpass theorem and a result due to Lions for critical growth.

• 出版日期2018-5