Neumann problems for second order ordinary differential equations across resonance
type: Item
instance of: scholarly article
title: Neumann problems for second order ordinary differential equations across resonance
zbMATH Open document ID: 0824.34029
DOI: 10.1007/BF01003558
author: Huaizhong Wang
author: Yong Li
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1995-08-10T00:00:00Z
review text: The boundary value problem \((*)\) \(y''+ f(t, y)= 0\), \((t, y)\in W= [0, 1]\times \mathbb{R}\), \(y'(0)= a\), \(y'(1)= b\) is considered. Some results concerning the unique solvability of \((*)\) are established. Here \(f\), \(f_ y\in C(W)\) and \(f\) belongs to the nearly-resonance domain: \(A\leq f_ y\leq \beta(t)\leq B\) for some \(k^ 2\pi^ 2< A< (k+ 1)^ 2 \pi^ 2\leq B< \infty\), \(\beta\in L[0, 1]\). By means of Pontryagin's maximum principle, the exact estimates, which guarantee the existence of a unique solution to the corresponding linearized BVP, are also obtained.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 49K15
zbMATH DE Number: 777683
zbMATH Keywords: boundary value problem
zbMATH Keywords: unique solvability
zbMATH Keywords: Pontryagin's maximum principle
reviewed by: Elena Trofimchuk
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 777683