TY - JOUR

T1 - Multiplicity of 1D-concentrated positive solutions to the Dirichlet problem for an equation with p-Laplacian

AU - Kolonitskii, S. B.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

U2 - 10.1007/s10688-015-0099-7

DO - 10.1007/s10688-015-0099-7

M3 - Article

VL - 49

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

SN - 0016-2663

IS - 2

ER -