Electron. J. Diff. Eqns., Vol. 2009(2009), No. 11, pp. 1-11.

Existence and uniqueness of positive solutions for a BVP with a p-Laplacian on the half-line

Yu Tian, Weigao Ge

Abstract:
In this work, we consider the second order multi-point boundary-value problem with a p-Laplacian
$$\displaylines{ (\rho(t)\Phi_p(x'(t)))'+f(t, x(t), x'(t))=0,\quad t\in [0,+\infty),\cr x(0)=\sum_{i=1}^{m}\alpha_i x(\xi_i), \quad \lim_{t\to\infty}x(t)=0\,. }$$
By applying a nonlinear alternative theorem, we establish existence and uniqueness of solutions on the half-line. Also a uniqueness result for positive solutions is discussed when $f$ depends on the first-order derivative. The emphasis here is on the one dimensional p-Laplacian operator.

Submitted May 23, 2008. Published January 9, 2009.
Math Subject Classifications: 34B10, 34B18, 34B40.
Key Words: Multi-point boundary-value problem; p-Laplacian; half-line; positive solutions; existence; uniqueness.

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Yu Tian
School of Science
Beijing University of Posts and Telecommunications
Beijing 100876, China
email: tianyu2992@163.com
Weigao Ge
Department of Mathematics
Beijing Institute of Technology
Beijing 100081, China
email: gew@bit.edu.cn

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