Existence for a class of nonlinear singular boundary value problems

Abstract

We establish existence of solutions of the Dirichlet problem under a variety of conditions by obtaining a priori bounds and using the topological transversality theorem. Here p(0) = 0 and p(a) = 0 are allowed, and q is not assumed to be continuous at 0 or at a, so the problem may be singular at either or both endpoints. We consider the superlinear as well as the subliner case.

In addition, under similar hypotheses we establish existence of solutions for the problem with the mixed boundary conditions .

Keywords:

• Existence
• nonlinear
• singular
• Dirichlet
• sublinear
• superlinear
• boundary value problem
• ordinary differential equations

AMS (MOS)::

• 34B15
• 34A34