Existence and multiplicity of boundary blow-up nonnegative solutions to two-point boundary value problems
This article is concerned with the existence and the multiplicity of boundary blow-up nonnegative solutions to nonlinear boundary value problems of the form \[ -u''(x) = \lambda f(u(x)), \quad 0 < x < 1, \qquad \lim_{x \rightarrow 0^{+}} u(x) = \lim_{x \rightarrow 1^{-}} u(x) = \infty, \] where \(\lambda\) is positive and \(f\) is a Lipschitz continuous function. The results presented here extend and improve some previous one obtained by \textit{V. Anuradha, Ch. Brown} and \textit{R. Shivaji} [Nonlinear Anal., Theory Methods Appl. 26, No. 3, 613-630 (1996; Zbl 0846.34015)]. Moreover, some numerical simulations are given.
scientific article; zbMATH DE number 1491642