Research
On symmetric positive homoclinic solutions of semilinear p-Laplacian differential equations
Author affiliations
Department of Mathematical Analysis, University of Ruse, Ruse, 7017, Bulgaria
Citation and License
Boundary Value Problems 2012, 2012:121 doi:10.1186/1687-2770-2012-121
Published: 24 October 2012Abstract
In this paper we study the existence of even positive homoclinic solutions for p-Laplacian ordinary differential equations (ODEs) of the type 
, where 
, 
and the functions a and b are strictly positive and even. First, we prove a result on symmetry of positive
solutions of p-Laplacian ODEs. Then, using the mountain-pass theorem, we prove the existence of
symmetric positive homoclinic solutions of the considered equations. Some examples
and additional comments are given.
MSC: 34B18, 34B40, 49J40.
