A Concentration Phenomenon for p-Laplacian Equation

作者：Zhong, Yansheng^*

来源：Journal of Applied Mathematics, 2014, 2014: 148902.

DOI：10.1155/2014/148902

• NONLINEAR SCHRODINGER-EQUATIONS
• MULTIPLE POSITIVE SOLUTIONS
• STANDING WAVES
• CRITICAL FREQUENCY
• EXISTENCE
• PRINCIPLES
• MAXIMUM

It is proved that if the bounded function of coefficient Q(n) in the following equation -div {vertical bar del u vertical bar(p-2)del u} + V(x)vertical bar u vertical bar(p-2) u = Q(n) (x)vertical bar u vertical bar(q-2)u, u(x) = 0 as x is an element of partial derivative Omega u(x) -> 0 as vertical bar x vertical bar -> infinity is positive in a region contained in Omega and negative outside the region, the sets {Q(n) > 0} shrink to a point x(0) is an element of Omega as n -> infinity 8, and then the sequence u(n) generated by the nontrivial solution of the same equation, corresponding to Q(n), will concentrate at x(0) with respect to W-0(1,p) (Omega) and certain L-2 (Omega)-norms. In addition, if the sets {Q(n) > 0} shrink to finite points, the corresponding ground states {u(n)} only concentrate at one of these points. These conclusions extend the results proved in the work of Ackermann and Szulkin (2013) for case p = 2.

• 出版日期2014
• 单位福建师范大学