Existence of solutions to boundary value problems for a nonlinear second order equation with weak Carathéodory functions
type: Item
instance of: scholarly article
title: Existence of solutions to boundary value problems for a nonlinear second order equation with weak Carathéodory functions
zbMATH Open document ID: 0891.34022
author: Junyu Wang
author: Wenjie Gao
published in: Differential Equations and Dynamical Systems
publication date: 1998-07-19T00:00:00Z
review text: The authors consider the following boundary value problems \[ [\phi(y')]'= f(x,y,y'),\quad a<x<b,\tag{1} \] \[ y(a)= A,\quad y(b)= B,\tag{2} \] \[ y'(a)= A,\quad y(b)= B,\tag{3} \] \[ [\phi(y')]'= f(x,y,y'),\quad a<x<+\infty,\quad y(a)= A,\tag{4} \] where \(A\) and \(B\) are prescribed real numbers. The authors prove the existence of solutions of problems (1), (2) and (1), (3) when \(\phi:\mathbb{R}\to\mathbb{R}\) is continuous and strictly increasing; \(f:I\times \mathbb{R}^2\to\mathbb{R}\) is a weak Carathéodory function and satisfies a Nagumo condition.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B10
zbMATH DE Number: 1098666
zbMATH Keywords: upper and lower solutions
zbMATH Keywords: weak Carathéodory function
zbMATH Keywords: Nagumo condition
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1098666