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Journal of Applied Mathematics and Stochastic Analysis
Volume 7 (1994), Issue 4, Pages 487-507
doi:10.1155/S1048953394000389

Existence principles for second order nonresonant boundary value problems

Donal O'Regan

University College Galway, Department of Mathematics, Galway, Ireland

Received 1 December 1993; Revised 1 April 1994

Copyright © 1994 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We discuss the two point singular “nonresonant” boundary value problem 1p(py′)′=f(t,y,py′) a.e. on [0,1] with y satisfying Sturm Liouville, Neumann, Periodic or Bohr boundary conditions. Here f is an L1-Carathéodory function and p∈C[0,1]∩C1(0,1) with p>0 on (0,1).