Positive Solutions for Semipositone (n,p) Boundary Value Problems

Xiaoming He and Weigao Ge

Abstract: This paper is concerned with the existence of positive solutions to the $(n,p)$ boundary value problem $$ \begin{array}{ll} u^{(n)}+\lambda\, f(t,u)=0,& 0<t<1,
u^{(i)}(0)=0,& 0\leq i\leq n-2,
u^{(p)}(1)=0,& 1\leq p\leq n-1, \end{array} $$ where $p$ is fixed and $\lambda >0$. We shall use a fixed point theorem in a cone to obtain positive solutions of the above problem for $\lambda$ on a suitable interval.

Keywords: (n,p) boundary value problem; positive solution; Krasnosel'skii fixed point theorem.

Classification (MSC2000): 34B15.

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