Geodesic
Three positive solutions for a system of singular generalized Lidstone problems
Electronic journal of differential equations, Tome 2009 (2009)
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.
Classification : 34A34, 34B18, 45G15, 47H10
Keywords: singular generalized lidstone problem, positive solution, cone, concave functional 
@article{EJDE_2009__2009__a161,
     author = {Xu,  Jiafa and Yang,  Zhilin},
     title = {Three positive solutions for a system of singular generalized {Lidstone} problems},
     journal = {Electronic journal of differential equations},
     year = {2009},
     volume = {2009},
     zbl = {1188.34034},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a161/}
}
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Xu,  Jiafa; Yang,  Zhilin. Three positive solutions for a system of singular generalized Lidstone problems. Electronic journal of differential equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a161/