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Positive solutions for a three-point boundary value problem at resonance. (English) Zbl 1125.34014

Summary: This paper deals with the second-order three-point boundary value problem \[ x''(t)=f(t,x(t)),\quad t\in(0,1), \]
\[ x'(0)=0,\quad x(\eta)= x(1). \] The existence and multiplicity of positive solutions are investigated by means of the fixed point theorem in cones.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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