A uniqueness result for a singular nonlinear eigenvalue problem

作者：Castro Alfonso^*; Ko Eunkyung; Shivaji R

来源：Proceedings of the Royal Society of Edinburgh: Section A Mathematics , 2013, 143(4): 739-744.

DOI：10.1017/S0308210512000418

We consider the positive solutions to singular boundary-value problems of the form %26lt;br%26gt;-Delta u = lambda f(u)/u(beta) in ohm, %26lt;br%26gt;u = 0 on partial derivative ohm, %26lt;br%26gt;where lambda %26gt; 0, beta is an element of (0, 1) and ohm is a bounded domain in R-N, N %26gt;= 1, with smooth boundary partial derivative ohm. Here, we assume that f : [0, infinity) -%26gt; (0, infinity) is a C-1 non-decreasing function and f(s)/s(beta) is decreasing for s large. We establish the uniqueness of the positive solution when lambda is large.

• 出版日期2013-8