Summary: Existence of Solutions for a One Dimensional
p-Laplacian on Time-Scales
DOUGLAS ANDERSONa,*, RICHARD AVERYb,
and JOHNNY HENDERSONc,
a
Department of Mathematics, Concordia College, Moorhead, MN 56562, USA;
b
College of Natural Sciences, Dakota State University, Madison, SD 57042, USA;
c
Department of Mathematics, Baylor University, Waco, TX 76798, USA
(Received 10 February 2003; Revised 19 January 2004; In final form 22 March 2004)
We prove the existence of at least one positive solution to the time-scale, delta­nabla dynamic equation, ðgðuD
ÞÞ7
þ
cðtÞ fðuÞ ¼ 0; with boundary conditions, uðaÞ 2 B0ðuD
ðnÞÞ ¼ 0 and uD
ðbÞ ¼ 0: Here, gðzÞ ¼ jzjp22
z for p . 1;
n [ (a,b), f and c are left-dense continuous and B0 is a function "bounded" by two linear rays.
Keywords: Fixed-point theorems; Delta­nabla dynamic equation; One-dimensional p-Laplacian; Multiple

Source: Anderson, Douglas R. - Department of Mathematics and Computer Science, Concordia College

Collections: Mathematics