Multiple solutions for nonhomogeneous Choquard equation involving Hardy-Littlewood-Sobolev critical exponent

作者：Shen, Zifei; Gao, Fashun; Yang, Minbo^*

来源：Zeitschrift fur Angewandte Mathematik und Physik, 2017, 68(3): 61.

DOI：10.1007/s00033-017-0806-8

• Choquard equation
• Nonhomogeneous
• Critical exponent
• Hardy-Littlewood-Sobolev inequality
• Multiple solutions

We consider the following critical nonhomogeneous Choquard equation @@@ -Delta u = (f(Omega) vertical bar u(y)vertical bar(2 mu)vertical bar x-y vertical bar(mu) dy) vertical bar-u vertical bar(2 mu)*(-2) u + lambda u + f(x) in Omega, @@@ where Omega is a smooth bounded domain of R-N, 0 in interior of Omega, lambda is an element of R, N >= 7, 0 < mu < N, 2(mu)* = ( 2N - mu)/( N - 2) is the upper critical exponent in the sense of the Hardy- Littlewood- Sobolev inequality, and f( x) is a given function. Using variational methods, we obtain the existence of multiple solutions for the above problem when 0 < lambda < lambda(1), where lambda(1) is the first eigenvalue of -Delta in H-0(1) (Omega).

• 出版日期2017-6
• 单位浙江师范大学