Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4617621 | Journal of Mathematical Analysis and Applications | 2012 | 15 Pages |
Abstract
In this paper, we prove the existence of multiple solutions for second order Sturm–Liouville boundary value problem{−Lu=f(x,u),x∈[0,1]\{x1,x2,…,xl},−Δ(p(xi)u′(xi))=Ii(u(xi)),i=1,2,…,l,R1(u)=0,R2(u)=0, where Lu=(p(x)u′)′−q(x)uLu=(p(x)u′)′−q(x)u is a Sturm–Liouville operator, R1(u)=αu′(0)−βu(0)R1(u)=αu′(0)−βu(0), R2(u)=γu′(1)+σu(1)R2(u)=γu′(1)+σu(1). The technical approach is fully based on lower and upper solutions and variational methods. The interesting point is that the property that the critical points of the energy functional are exactly the fixed points of an operator that involves the Greenʼs function. Besides, the existence of four solutions is given.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Yu Tian, Weigao Ge,