Existence to singular boundary value problems with sign changing nonlinearities using an approximation method approach期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Existence to singular boundary value problems with sign changing nonlinearities using an approximation method approach

Authors:

Haishen Lü Donal O’Regan Ravi P. Agarwal

Affiliation:

(1) Department of Applied Mathematics, Hohai University, Nanjing, 210098, P. R. China;(2) Department of Mathematics, National University of Ireland, Galway, Ireland;(3) Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901-6975, USA

Abstract:

This paper studies the existence of solutions to the singular boundary value problem

$$left{ begin{gathered} - u' = g(t,u) + (h,u),t in (0,1), hfill u(0) = 0 = u(1), hfill end{gathered} right.$$

, where g: (0, 1) × (0, ∞) → ℝ and h: (0, 1) × [0, ∞) → [0, ∞) are continuous. So our nonlinearity may be singular at t = 0, 1 and u = 0 and, moreover, may change sign. The approach is based on an approximation method together with the theory of upper and lower solutions. The research is supported by NNSF of China(10301033).

Keywords:

singular boundary value problem positive solution upper and lower solution

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