On the Existence of Positive Solutions of Ordinary Differential Equations
Open Access
- 1 March 1994
- journal article
- Published by JSTOR in Proceedings of the American Mathematical Society
- Vol. 120 (3), 743-748
- https://doi.org/10.2307/2160465
Abstract
We study the existence of positive solutions of the equation <!-- MATH ${u^{''}} + a(t)f(u) = 0$ --> with linear boundary conditions. We show the existence of at least one positive solution if is either superlinear or sublinear by a simple application of a Fixed Point Theorem in cones.
Keywords
This publication has 13 references indexed in Scilit:
- Semilinear elliptic problems in annular domainsZeitschrift für angewandte Mathematik und Physik, 1989
- Existence and uniqueness results for semi-linear Dirichlet problems in annuliArchive for Rational Mechanics and Analysis, 1989
- Existence of positive radial solutions for semilinear elliptic equations in the annulusJournal of Differential Equations, 1987
- Nonlinear elliptic problems in annular domainsJournal of Differential Equations, 1987
- Positive Solution of a Problem of Emden–Fowler Type with a Free BoundarySIAM Journal on Mathematical Analysis, 1987
- Nonlinear Functional AnalysisPublished by Springer Science and Business Media LLC ,1985
- Nonzero solutions of boundary value problems for second order ordinary and delay-differential equationsJournal of Differential Equations, 1972
- Boundary value problems for ordinary differential equationsRocky Mountain Journal of Mathematics, 1971
- Positive Solutions of Operator Equations.The American Mathematical Monthly, 1967
- Nonoscillation Theorems For a Class of Nonlinear Differential EquationsTransactions of the American Mathematical Society, 1959