Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 11, pp. 1-11.
Title: Existence and uniqueness of positive solutions for a
BVP with a p-Laplacian on the half-line
Authors: Yu Tian (Beijing Univ. of Posts and Telecom., China)
Weigao Ge (Beijing Institute of Technology, China)
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 09, 2009.
Math Subject Classifications: 34B10, 34B18, 34B40.
Key Words: Multi-point boundary-value problem; p-Laplacian;
half-line; positive solutions; existence; uniqueness.