On symmetric positive homoclinic solutions of semilinear p-Laplacian differential equations
Department of Mathematical Analysis, University of Ruse, Ruse, 7017, Bulgaria
Boundary Value Problems 2012, 2012:121 doi:10.1186/1687-2770-2012-121Published: 24 October 2012
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.