Studies On The Existence Of Solutions To Several Kinds Of Kirchhoff-Schr(?)dinger Type Systems

In this paper,we discuss the existence of multiple solutions of several kinds of KirchhoffSchr(?)dinger-Poisson system by using variational method.The first chapter mainly introduces the historical background and significance of the research,the research status at home and abroad,the work done in this paper.In the second chapter,we study the existence of ground state solutions for fractional Schr(?)dinger-Kirchhoff-Poisson systems with general nonlinearities:#12 where#12 s,t ?(0,1)with 2t+4s>3,0<?<3-2t,f:R3 ×R?R satisfies a Caratheodory condition,and(-?)s is the fractional Laplace operator which up to a nonrmalization constant,defined as#12 along functions ??C0?(R3),B?(x)denotes the ball of R3 centered at x ?R3 and with radius ?>0.Firstly we give some suitable assumptions about f,then proving existence of nontrivial solutions to above equation by using variational methods and Pohozaev identity.In the third chapter,we consider the existence of the following Schr(?)dinger-Choquard-Kirchhofftype equation:M[u]s,pp(-?)psu+V(x)|u|p-2u=?(I?*|u|ps,?*)|u|ps,?*-2U+?k(x)|u|q-2u,x?RN.where(-?)ps is the fractional p-Laplacian operator,[u]s,p is the Gagliardo p-seminorm,0<s<1<p<?,N>sp,1<q<p,M is a continuous and positive function,V is a continuous and positive potential function and k(x)is a non-negative function in an appropriate Lebesgue space.Combining the concentration-compactness principle in fractional Sobolev space and Kajikiya's new version of symmetric mountain pass lemma,we obtain the existence of infinitely many solutions for suitable positive parameters ? and ?.