Iterative procedures for nonlinear second order boundary value problems
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.
scientific article; zbMATH DE number 4204822
scientific article