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

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).