Multiplicity of 1D-concentrated positive solutions to the Dirichlet problem for an equation with p-Laplacian

作者：Kolonitskii S B^*

来源：Functional Analysis and Its Applications, 2015, 49(2): 151-154.

DOI：10.1007/s10688-015-0099-7

• p-Laplacian
• multiplicity of solutions

We consider the Dirichlet problem for the equation -Delta (p) = u (q-1) with (p-)Laplacian in a thin spherical annulus in a"e (n) with 1 < p < q p* (n-1), where p* (n-1) is the critical Sobolev exponent for embedding in a"e (n-1) and either n = 4 or n a (c) 3/4. We prove that this problem has a countable set of solutions concentrated in neighborhoods of certain curves. Any two such solutions are nonequivalent if the annulus is thin enough. As a corollary, we prove that the considered problem has as many solutions as required, provided that the annulus is thin enough.

• 出版日期2015-4