In this paper, we consider a class of fractional Schrödinger–Poisson systems (Formula presented.) and (Formula presented.) in (Formula presented.), where (Formula presented.) with (Formula presented.), (Formula presented.) denotes a parameter, (Formula presented.) admits a potential well (Formula presented.) and (Formula presented.) is the fractional Sobolev critical exponent. Given some reasonable assumptions as to the potential V and the nonlinearity f, with the help of a constrained manifold argument, we conclude the existence of positive ground state solutions for some sufficiently large (Formula presented.). Upon relaxing the restrictions on V and f, we utilize the minimax technique to show that the system has a positive mountain-pass type by introducing some analytic tricks. Moreover, we investigate the asymptotical behavior of the obtained solutions when (Formula presented.).
Shen, L., Squassina, M., Concentrating Solutions for Fractional Schrödinger–Poisson Systems with Critical Growth, <<FRACTAL AND FRACTIONAL>>, 2024; 8 (10): 1-24. [doi:10.3390/fractalfract8100581] [https://hdl.handle.net/10807/311336]
Concentrating Solutions for Fractional Schrödinger–Poisson Systems with Critical Growth
Squassina, Marco
2024
Abstract
In this paper, we consider a class of fractional Schrödinger–Poisson systems (Formula presented.) and (Formula presented.) in (Formula presented.), where (Formula presented.) with (Formula presented.), (Formula presented.) denotes a parameter, (Formula presented.) admits a potential well (Formula presented.) and (Formula presented.) is the fractional Sobolev critical exponent. Given some reasonable assumptions as to the potential V and the nonlinearity f, with the help of a constrained manifold argument, we conclude the existence of positive ground state solutions for some sufficiently large (Formula presented.). Upon relaxing the restrictions on V and f, we utilize the minimax technique to show that the system has a positive mountain-pass type by introducing some analytic tricks. Moreover, we investigate the asymptotical behavior of the obtained solutions when (Formula presented.).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.