On symmetric positive homoclinic solutions of semilinear p-Laplacian differential equations

被引：0
作者：
Stepan Tersian
机构：
[1] University of Ruse,Department of Mathematical Analysis
来源：
Boundary Value Problems | / 2012卷
关键词：
-Laplacian ODEs; homoclinic solution; weak solution; Palais-Smale condition; mountain-pass theorem;
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摘要：
In this paper we study the existence of even positive homoclinic solutions for p-Laplacian ordinary differential equations (ODEs) of the type (u′|u′|p−2)′−a(x)u|u|p−2+λb(x)u|u|q−2=0, where 2≤p<q, λ>0 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.
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