IJPAM: Volume 98, No. 3 (2015)

POSITIVE SOLUTIONS FOR
NONLINEAR EIGENVALUE PROBLEMS

Hongyan Guan$^1$, Yan Hao$^2$
$^{1,2}$School of Mathematics and Systems Science
Shenyang Normal University
Shenyang, 110034, P.R. CHINA


Abstract. In this paper, by using the Krasnoselskii fixed point theorem, we investigate the existence of positive solutions for the following nonlinear eigenvalue problem:

\begin{displaymath} \left\{\begin{aligned}&u''(t)+a(t)u'(t)+b(t)u(t)+\lambda h(t... ...u(t_1)=0, \quad \alpha u(\eta)=u(t_2), \end{aligned}\right.\\ \end{displaymath}

where $t_1<\eta<t_2$ and $0<\alpha\phi_1(\eta)<1$ and $\phi_1$ is the unique solution of the linear boundary value problem:

\begin{displaymath} \left\{\begin{aligned} &u''(t)+a(t)u'(t)+b(t)u(t)=0,\quad t\in [t_1,t_2],\\ &u(t_1)=0,\quad u(t_2)=1. \end{aligned}\right. \end{displaymath}



Received: October 6, 2014

AMS Subject Classification: 34B15

Key Words and Phrases: positive solution, nonlinear eigenvalue problem, cone, fixed point

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DOI: 10.12732/ijpam.v98i3.9 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 98
Issue: 3
Pages: 365 - 374


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