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EIGENVALUE PROBLEMS FOR SYSTEMS OF NONLINEAR HIGHER ORDER BOUNDARY VALUE PROBLEMS  

Rao, A. Kameswara (Department of Applied Mathematics, Andhra University)
Rao, S. Nageswara (Department of Mathematics, Sri Prakash College of Engineering)
Publication Information
Journal of applied mathematics & informatics / v.28, no.3_4, 2010 , pp. 711-721 More about this Journal
Abstract
Values of the parameter $\lambda$ are determined for which there exist positive solutions of the system of boundary value problems, $u^{(n)}+{\lambda}p(t)f(\upsilon)=0$, $\upsilon^{(n)}+{\lambda}q(t)g(u)=0$, for $t\;{\in}\;[a,b]$, and satisfying, $u^{(i)}(a)=0$, $u^{(\alpha)}(b)=0$, $\upsilon^{(i)}(a)=0$, $\upsilon^{(\alpha)}(b)=0$, for $0\;{\leq}\;i\;{\leq}\;n-2$ and $1\;{\leq}\;\alpha\;\leq\;n-1$ (but fixed). A well-known Guo-Krasnosel'skii fixed point theorem is applied.
Keywords
System of differential equations; two-point boundary value problem; eigenvalue problem; positive solution; cone;
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