Iterative procedures for nonlinear second order boundary value problems
type: Item
instance of: scholarly article
title: Iterative procedures for nonlinear second order boundary value problems
zbMATH Open document ID: 0729.34013
DOI: 10.1007/BF01765310
author: Paul Waltman
author: Juan A. Gatica
author: Vladimir I. Oliker
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1990-01-01T00:00:00Z
review text: Questions of the existence of positive solutions of the nonlinear BVP with parameter \(\lambda\) and separated boundary conditions of the form \(y''+\lambda f(x,y)=0,\alpha y(0)-\beta y'(0)=0,\gamma y(1)+\delta y'(1)=0,\) are studied. For nonlinear differential equations the values of \(\lambda\) for which there is a nontrivial solution need not be discrete. An important way in which the results of this paper differ from those, e.g. of \textit{C. D. Luning} and \textit{W. L. Perry} [Q. Appl. Math. 35, 257- 268 (1977; Zbl 0363.34014)] is that the authors seek a solution for a fixed value of the parameter. The paper focuses on iterative techniques for the super and sublinear problems to find positive solutions within a prescribed region.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34A45
zbMATH DE Number: 4204822
zbMATH Keywords: positive solutions
zbMATH Keywords: nonlinear BVP
zbMATH Keywords: iterative techniques
reviewed by: Rolf-Dieter Reiss
MaRDI profile type: Publication
cites work: Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
cites work: R-curvature, estimates and the stability of solutions of the Dirichlet problem for elliptic equations
cites work: Le nombre de solutions de certains problèmes semi-linéaires elliptiques
cites work: Q5789040
cites work: Q5555879
cites work: Existence, Uniqueness, and Spectral Properties of Nonlinear Eigenvalue Problems
cites work: Q5533540
cites work: Q5606061
cites work: Implementation of new iterative techniques for solutions of Thomas-Fermi and Emden-Fowler equations
cites work: Subfunction and second-order ordinary differential inequalities
cites work: Q5531285
cites work: On the Existence of Positive Solutions of Semilinear Elliptic Equations
cites work: An iterative technique for solution of the Thomas-Fermi equation utilizing a nonlinear eigenvalue problem
cites work: Convergence of Berryman’s iterative method for some Emden–Fowler equations
cites work: Positive Solutions of Negative Exponent Generalized Emden–Fowler Boundary Value Problems
cites work: Iterative solution of a nonlinear boundary value problem for a rotating string
cites work: Q3285773
cites work: A Superlinear Sturm-Liouville Problem
cites work: SOLUTIONS OF LARGE NORM FOR NON-LINEAR STURM-LIOUVILLE PROBLEMS
cites work: Nonlinear Sturm-Liouville problems
cites work: Superlinear Sturm-Liouville problems
cites work: On the Generalized Emden–Fowler Equation
description: scientific article; zbMATH DE number 4204822