【摘要】：本文首先研究如下帶有積分-微分算子的一般非局部問題其中Ω是RN中具有Lipschitz邊界的有界區(qū)域,LK是積分-微分算子.利用約束極小和定量形變引理,我們證明了上述問題至少存在一個變號基態(tài)解(指所有變號解中具有最低能量的解)且其能量嚴格大于基態(tài)解的能量.其次,我們研究了上述問題帶有凹凸非線性項即的情形,其中1q2p2s*:= N2,N2s,s ∈(0,1).利用噴泉定理及其對偶形式我們獲得了無窮多解的存在性結(jié)果.最后,我們考慮如下分數(shù)階Kirchhoff問題基態(tài)解的存在性和集中現(xiàn)象其中M(t)=ε2sa + ε4s-3bt是Kirchhoff函數(shù),0s1,ε0是充分小的參數(shù),V是能達到全局極小值、正的連續(xù)位勢,f在無窮遠處超3次但次臨界增長.當ε0充分小時,我們證明了上述分數(shù)階Kirchhoff問題基態(tài)解的存在性.其次,我們建立了在ε→0+時基態(tài)解的收斂性、集中性以及衰減估計.
[Abstract]:In this paper, we first study the following general nonlocal problems with integro-differential operators, where 惟 is a bounded domain of RN with Lipschitz boundary and LK is an integro-differential operator. By using constrained minima and quantitative deformation Lemma, we prove that there exists at least one solution of the ground state of the above problem (that is, the solution with the lowest energy) and that the energy of the solution is strictly larger than that of the solution of the ground state. Secondly, we study the case of the above problem with concave and convex nonlinear terms, where 1q2p2sn = N 2n 2s n 2s 鈭，

本文編號：2242002