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Positive solutions to superlinear semipositone periodic boundary value problems with repulsive weak singular forces. (English) Zbl 1105.34306

Summary: This paper is devoted to study the existence of positive solutions to the second-order semipositone periodic boundary value problem \[ x''+ a(t)x=f(t,x),\;x(0)=x(1),\quad x'(0)=x'(1). \] Here, \(f(t,x)\) may be singular at \(x=0\) and may be superlinear at \(x=+\infty\). Our analysis relies on a fixed-point theorem in cones.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B16 Singular nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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