Electron. J. Diff. Eqns., Vol. 2007(2007), No. 20, pp. 1-10.

Positive solutions for a class of nonresonant boundary-value problems

Xuemei Zhang

Abstract:
This paper concerns the existence and multiplicity of positive solutions to the nonresonant second-order boundary-value problem
$$ Lx=\lambda w(t)f(t,x). $$
We are interested in the operator $Lx:=-x''+\rho qx$ when $w$ is in $L^{p}$ for $1\leq p \leq +\infty$. Our arguments are based on fixed point theorems in a cone and Holder's inequality. The nonexistence of positive solutions is also studied.

Submitted November 28, 2006. Published January 27, 2007.
Math Subject Classifications: 34B15.
Key Words: Positive solution; fixed point theorem; existence; complete continuity.

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Xuemei Zhang
Department of Mathematics and Physics
North China Electric Power University
Beijing 102206, China
email: zxm74@sina.com

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