Generalized Ambrosetti-Prodi conditions for nonlinear two-point boundary value problems
type: Item
instance of: scholarly article
title: Generalized Ambrosetti-Prodi conditions for nonlinear two-point boundary value problems
zbMATH Open document ID: 0646.34022
DOI: 10.1016/0022-0396(87)90127-6
author: R. Nugari
author: Raffaele Chiappinelli
author: Jean Mawhin
published in: Journal of Differential Equations
publication date: 1987-01-01T00:00:00Z
review text: For the following two-point boundary value problem \[ (P)\quad u''+f(x,u)=s(\frac{2}{\pi})^{1/2}\sin (x),\quad u(0)=u(\pi)=0 \] where f is a continuous function satisfying the condition (H) \(\lim_{| u| \to \infty}f(x,u)=+\infty\) it is shown that there exist real numbers \(so\leq so^+\) such that (1) for \(s<so\), (P) has no solution; (2) for \(s\in [so,so^+]\) (P) has at least one solution; (3) for \(s>so^ olution\) u(t), \(t\in [0,\infty [\). Theorem 1 states that Kiguradze- Kvinikadze condition cannot replace the condition \(J_{p\phi}=\int^{\infty}_{0}p(\tau)\phi^{-1}(\tau)\tau^{(n- 1)\lambda}d\tau <\infty,\) where \(\phi\) (t)\(\to \infty\) under \(t\to \infty\). The authors investigate case \(I_{p\phi}=\infty\).
Mathematics Subject Classification ID: 34B10
zbMATH DE Number: 4054072
zbMATH Keywords: second order differential equation
MaRDI profile type: Publication
full work available at URL: 0022-0396(87)90127-6
OpenAlex ID: W2092149023
cites work: On the inversion of some differentiable mappings with singularities between Banach spaces
cites work: Q3901881
cites work: Q4095271
cites work: Q3333438
cites work: On the superlinear Ambrosetti-Prodi problem
cites work: A Variational approach to superlinear elliptic problems
cites work: A Multiplicity Result for Periodic Solutions of Forced Nonlinear Second order Ordinary Differential Equations
cites work: Q3821008
cites work: Remarks on some quasilinear elliptic equations
cites work: On the number of solutions of a nonlinear Dirichlet problem
cites work: Q3962049
cites work: Q5187549
cites work: Q5185183
description: scientific article; zbMATH DE number 4054072