Existence and Non-Existence of Positive Solutions of BVPs for Singular ODEs on Whole Lines

• Journal title : Kyungpook mathematical journal
• Volume 55, Issue 4,  2015, pp.997-1030
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2015.55.4.997
Title & Authors
Existence and Non-Existence of Positive Solutions of BVPs for Singular ODEs on Whole Lines
LIU, YUJI; YANG, PINGHUA;

Abstract
This paper is concerned with integral type boundary value problems of second order singular differential equations with quasi-Laplacian on whole lines. Sufficient conditions to guarantee the existence and non-existence of positive solutions are established. The emphasis is put on the non-linear term $\small{[{\Phi}({\rho}(t)x^{\prime}(t))}$$\small{]}$$\small{^{\prime}}$ involved with the nonnegative singular function and the singular nonlinearity term f in differential equations. Two examples are given to illustrate the main results.
Keywords
Second order singular differential equation;integral type boundary value problem;positive solution;fixed point theorem;
Language
English
Cited by
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