A priori bounds for solutions to nonlinear two-point boundary value problems
- 1 January 1973
- journal article
- research article
- Published by Taylor & Francis in Applicable Analysis
- Vol. 3 (2) , 157-167
- https://doi.org/10.1080/00036817308839062
Abstract
The boundary value problem is considered. The function f is assumed to be continuous on [a, b]× R2, and g 1 and g 2 are assumed to be continuous and nondecreasing on R. The condition (A)There exists M 1 >0 and a positive, continuous function Ψ(p) defined on [0, ∞) such that and for , is used to obtain an a priori bound on solutions, As applications of the a priori bound, an existence theorem is obtained using the Leray-Schauder Theorem, and a “weak continuous dependence theorem” is proved, In both cases, the well-known Nagumo condition is also imposed in order to obtain a priori bounds on derivatives of solutions.Keywords
This publication has 8 references indexed in Scilit:
- A nonlinear boundary value problemJournal of Differential Equations, 1970
- Nonlinear boundary value problems for second order differential equationsJournal of Differential Equations, 1970
- A nonlinear boundary value problemJournal of Differential Equations, 1968
- Solutions of second order ordinary differential equationsJournal of Differential Equations, 1968
- A generalized two-point boundary value problemProceedings of the American Mathematical Society, 1968
- Comparison theorems for nonlinear differential equationsJournal of Differential Equations, 1967
- A nonlinear boundary value problemBulletin of the American Mathematical Society, 1967
- Topologie et équations fonctionnellesAnnales Scientifiques de lʼÉcole Normale Supérieure, 1934