A general existence theorem for positive solutions to singular second order ordinary and functional differential equations (Q2709180)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: A general existence theorem for positive solutions to singular second order ordinary and functional differential equations |
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A general existence theorem for positive solutions to singular second order ordinary and functional differential equations |
scientific article |
Statements
3 February 2002
0 references
existence theorem
0 references
positive solutions
0 references
singular functional-differential equation
0 references
boundary value problem
0 references
fixed-point theorem
0 references
A general existence theorem for positive solutions to singular second order ordinary and functional differential equations (English)
0 references
The authors consider the singular equations \(u^{\prime \prime }(t)+g(t)f(u(t))=0 \)and \(u^{\prime \prime }(t)+g(t)f(u(w(t)))=0\), when \(G(.,.)g(.)\in L^{1}(0,1).\) They give a general existence result and \(f\) does not behave to suplinear or sublinear. Their result improve and extend many known results as those in [\textit{H. Wang}, J. Differ. Equations 109, No. 1, 1-7 (1994; Zbl 0798.34030); \textit{D. Guo}, J. Math. Res. Expo. 4, No. 1, 55-60 (1984; Zbl 0556.34010); \textit{Z. Guo}, Nonlinear Anal., Theory Methods Appl. 16, No. 9, 781-790 (1991; Zbl 0737.35024), and \textit{K. Lan} and \textit{R. L. Webb}, J. Differ. Equations 148, No. 2, 407-421 (1998; Zbl 0909.34013)].
0 references
