Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5024544 | Nonlinear Analysis: Theory, Methods & Applications | 2017 | 26 Pages |
Abstract
The paper is concerned with existence, multiplicity and asymptotic behavior of nonnegative solutions for a fractional Schrödinger-Poisson-Kirchhoff type system. As a consequence, the results can be applied to the special case (a+bâuâ2)[(âÎ)su+V(x)u]+Ïk(x)|u|pâ2u=λh(x)|u|qâ2u+|u|2sââ2uinR3,(âÎ)tÏ=k(x)|u|pinR3,âuâ=â«R3â«R3|u(x)âu(y)|2|xây|3+2sdxdy+â«R3V(x)|u|2dx1â2,where a,bâ¥0 are two numbers, with a+b>0, 1
0 is a parameter, s,tâ(0,1), (âÎ)s is the fractional Laplacian, kâL63+2tâp(3â2s)(R3) may change sign, V:R3â[0,â) is a potential function, 2sâ=6â(3â2s) is the critical Sobolev exponent, 1
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Authors
Mingqi Xiang, Fuliang Wang,