Existence of solutions to \((k,n-k-2)\) boundary value problems
type: Item
instance of: scholarly article
title: Existence of solutions to \((k,n-k-2)\) boundary value problems
zbMATH Open document ID: 0929.34020
DOI: 10.1016/S0096-3003(98)10046-2
author: Ravi P. Agarwal
author: Fu-Hsiang Wong
published in: Applied Mathematics and Computation
publication date: 2000-02-02T00:00:00Z
review text: The boundary value problem considered has the form \[ u^{(n)}(t)+ f\bigl(t,u(t), u'(t), \dots,u^{(n-2)} (t)\bigr)=0, \quad t\in(0,1), \] \[ u^{(r_i-1)}(0)=0,\;1\leq i\leq k,\quad u^{(s_j-1)}(1)=0,\;1\leq j\leq n-k-2, \] \[ \alpha u^{(n-2)}(0)-\beta u^{(n-1)}(0)=0,\quad\gamma u^{(n-2)}(1)+\delta u^{(n-1)} (1)= 0. \] Here, \(\{r_1,\dots,r_k\}\) and \(\{s_1,\dots,s_{n-k-2}\}\) are disjoint sets whose union is \(\{1,\dots,n-2\}\). Sufficient conditions for existence and nonuniqueness of solutions are given. Results of J. Mawhin and M. A. Krasnosel'skij are employed in the proofs.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B27
zbMATH DE Number: 1311051
zbMATH Keywords: higher-order ordinary differential equations
zbMATH Keywords: nonlinear boundary value problems
zbMATH Keywords: existence
zbMATH Keywords: nonuniqueness
reviewed by: Sergei A. Brykalov
MaRDI profile type: Publication
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full work available at URL: s0096-3003(98)10046-2
OpenAlex ID: W2083819536
description: scientific article; zbMATH DE number 1311051