Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 11, pp. 1-8.
Title: Existence of positive solutions for self-adjoint
boundary-value problems with integral boundary conditions
at resonance
Authors: Aijun Yang (Zhejiang Univ. of Technology, China)
Bo Sun (Central Univ. of Finance and Economics, Beijing, China)
Weigao Ge (Beijing Institute of Technology, Beijing, China)
Abstract:
In this article, we study the self-adjoint second-order
boundary-value problem with integral boundary conditions,
$$\displaylines{
(p(t)x'(t))'+ f(t,x(t))=0,\quad t\in (0,1),\cr
p(0)x'(0)=p(1)x'(1),\quad x(1)=\int_0^1x(s)g(s)ds,
}$$
which involves an integral boundary condition.
We prove the existence of positive solutions
using a new tool: the Leggett-Williams norm-type theorem
for coincidences.
Submitted September 29, 2010. Published January 20, 2011.
Math Subject Classifications: 34B10, 34B15, 34B45.
Key Words: Boundary value problem; resonance; cone;
positive solution; coincidence.