Geodesic
Three positive solutions for a system of singular generalized Lidstone problems
Electronic Journal of Differential Equations, Tome 2009 (2009).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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__a61,
     author = {Xu, Jiafa and Yang, Zhilin},
     title = {Three positive solutions for a system of singular generalized {Lidstone} problems},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2009},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a61/}
}
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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__a61/