MULTIPLICITY RESULTS FOR CLASSES OF SINGULAR PROBLEMS ON AN EXTERIOR DOMAIN

作者：Ko Eunkyoung^*; Lee Eun Kyoung; Shivaji R

来源：Discrete and Continuous Dynamical Systems, 2013, 33(11-12): 5153-5166.

DOI：10.3934/dcds.2013.33.5153

• Singular p-Laplacain problem
• positive radial solution
• multilpicity
• exterior domain
• sub-supersolution

We study radial positive solutions to the singular boundary value problem %26lt;br%26gt;[GRAPHICS] %26lt;br%26gt;where Delta(p)u = div (vertical bar del u vertical bar(p-2)del u), 1 %26lt; p %26lt; N, N %26gt; 2, lambda %26gt; 0, 0 %26lt;= beta %26lt; 1, Omega = {x is an element of R-N : vertical bar x vertical bar %26gt; r(0)} and r(0) %26gt; 0. Here integral : [0, infinity) -%26gt; (0, infinity) is a continuous nondecreasing function such that lim(u -%26gt;infinity) f(u)/u(beta)+p-1=0 and K is an element of C((r(0), infinity), (0, infinity)) is such that integral(infinity)(ro) r(mu) K (r)dr %26lt; infinity, for some mu %26gt; p - 1. We establish the existence of multiple positive solutions for certain range of lambda when f satisfies certain additional assumptions. A simple model that will satisfy our hypotheses is f (u) = e alpha u/alpha+u for alpha %26gt;%26gt; 1. We also extend our results to classes of systems when the nonlinearities satisfy a combined sublinear condition at infinity. We prove our results by the method of sub-super solutions.

• 出版日期2013-12