Electron. J. Diff. Eqns., Vol. 2009(2009), No. 89, pp. 1-12.

Existence of multiple positive solutions for third-order boundary-value problem on the half-line with dependence on the first order derivative

Sihua Liang, Jihui Zhang

Abstract:
By using fixed-point theorem for operators on a cone, sufficient conditions for the existence of multiple positive solutions for a third-order boundary-value problem on the half-line are established. In the case of the p-Laplace operator our results for p>1 generalize previous known results. The interesting point lies in the fact that the nonlinear term is allowed to depend on the first order derivative u'.

Submitted March 26, 2009. Published July 27, 2009.
Math Subject Classifications: 34B18, 34B40.
Key Words: Third-order boundary-value problems; positive solutions; half-line; fixed-point index theory.

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Sihua Liang
Institute of Mathematics, School of Mathematical Sciences
Nanjing Normal University, 210097, Jiangsu, China.
College of Mathematics, Changchun Normal University
Changchun 130032, Jilin, China
email: liangsihua@163.com
Jihui Zhang
Institute of Mathematics, School of Mathematical Sciences
Nanjing Normal University, 210097, Jiangsu, China
email: jihuiz@jlonline.com

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