Existence of solutions for fractional Choquard-Kirchhoff type problems with critical growth
In this paper,the fractional Choquard-Kirchhoff type problems on unbounded domains are consid-ered.These problems stem from the tension arising from nonlocal measurements of length of a string during transverse vibration and can also be used to describe the self-gravitational collapse of a quantum mechanical wave function.In the problem,the critical term μ(Iα*|u|2*α,s)|u|2*α,s-2 u and perturbation term λf(x)uq-1 are contained in the nonlinear terms,where μ,λ are positive parameters,2*α,s is the fractional Hardy-Littlewood-Sobolev critical exponent,and f(x)is a continuous function.First,the Palais-Smale sequences of energy functional corresponding to the problem are obtained by using the Nehari manifold and Ekeland's variational principle.Second,the upper bound of parameter μ is estimated.When appropriate ranges on the parameter λ and power q are chosen,the existence and multiplicity of positive solutions of the problem are further ob-tained by adopting the Vitali theorem and mountain pass lemma.Finally,when the parameter λ is sufficiently large,by using the strong maximum principle and critical point theorem,existence theorems for the positive solutions and infinitely many pairs of different solutions of the problem are established.
Fractional Choquard-Kirchhoff type problemHardy-Littlewood-Sobolev critical exponentNe-hari manifold
国家科技期刊平台
NSTL
万方数据
