Three positive solutions for a system of singular generalized Lidstone problems

• Main Authors: Jiafa Xu, Zhilin Yang
• Format: Article
• Language: English
• Published: Texas State University 2009-12-01
• Series: Electronic Journal of Differential Equations
• Subjects: Singular generalized Lidstone problem; positive solution; cone; concave functional
• Online Access: http://ejde.math.txstate.edu/Volumes/2009/163/abstr.html

In this article, we show the existence of at least three positive solutions for the system of singular generalized Lidstone boundary value problems $displaylines{ (-1)^m x^{(2m)}=a(t)f_1(t,x,-x'',dots,(-1)^{m-1}x^{(2m-2)},y,-y'',cr dots,(-1)^{n-1}y^{(2n-2)}), cr (-1)^n y^{(2n)}=b(t)f_2(t,x,-x'',dots,(-1)^{m-1}x^{(2m-2)},y,-y'',cr dots,(-1)^{n-1}y^{(2n-2)}), cr a_1 x^{(2i)}(0)-b_1 x^{(2i+1)}(0)=c_1x^{(2i)}(1)+d_1 x^{(2i+1)}(1)=0,cr a_2y^{(2j)}(0)-b_2y^{(2j+1)}(0)=c_2y^{(2j)}(1)+d_2y^{(2j+1)}(1)=0. }$$ The proofs of our main results are based on the Leggett-Williams fixed point theorem. Also, we give an example to illustrate our results.