Eigenvalue characterization for ( n, p) boundary-value problems

Patricia J. Y. Wong
Division of Mathematics
Nanyang Technological University
469 Bokit Timah Road
Singapore 259756
and
Ravi P. Agarwal
Department of Mathematics
National University of Singapore
10 Kent Ridge Crescent
Singapore 119260

Abstract:

We consider the (n, p) boundary value problem
$\begin{gather*}y^{(n)}+\lambda H(t,y)= \lambda K(t,y),\quad n\geq 2, \ t\in (0,1),\\ y^{(p)}(1)=y^{(i)}(0)=0,\quad 0\leq i\leq n-2, \end{gather*}$
where $\lambda> 0$ and $0\leq p\leq n -1$ is fixed. We characterize the values of $\lambda$ such that the boundary value problem has a positive solution. For the special case $\lambda =1$ , we also offer sufficient conditions for the existence of positive solutions of the boundary value problem.

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TeXAdel Scientific Publishing
26/04/2000