The Existence Of Bounded Radial Solutions And Sign-Changing Solutions For A Generalized Quasilinear Choquard Equation

In this dissertation,we mainly study the existence of bounded radial solutions and signchanging solutions for a class of quasilinear Choquard equations.By using the interation between the norm ‖·‖X and the standard one on W_1,p（R^N）,we study the existence of critical points confined to the radial function subspace X_r is studied by using the generalized AmbrosettiRabinowitz mountain road theorem.Then,the existence of infinitely sign-changing solutions of this problem is studied by using the method of invariant sets of descending flow,perturbation method and truncation technique,which includes the following three chapters:In Chapter one,we mainly introduce the physical background and the research status at home and abroad of Choquard equation,as well as the preliminary knowledge and notations,and then States the main results of this paper.In Chapter two,we study the following quasilinear Choquard equation-div（A（x,u）|▽u|P-2▽u）+1/pAt（x,u）|▽u|p+|u|P-2u=λ（Iα*|u|q）u|q-2u,x∈R^N,where A（x,t）is given real functions on R^N × R and At（x,t）=?/?tA（x,t）with N>3.0<α<N,p>1,p（N+α）/2N<q<p（N+α）/2（N-p）,λ≥0 is a parmeter.Under appropriate assumptions（A0）-（A5）,we obtained the existence of bounded radial solutions to the above problems.In Chapter three,we consider the following quasilinear Choquard equation where N≥ 3,1<p<N,max N-2p,1}<α<N,p ≤q<pα*=p（N+α）/2（N-p）,ε>0 is a small parameter.Under the assumption that the condition（A0）-（A4）holds and the potential function V（x）is bounded,the existence of infinitely variable sign-changing solutions to the above problems is obtained,and it is proved that these solutions are concentrated near the critical point.