Geodesic
Existence of positive solutions for self-adjoint boundary-value problems with integral boundary conditions at resonance
Electronic Journal of Differential Equations, Tome 2011 (2011).

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

Summary: In this article, we study the self-adjoint second-order boundary-value problem with integral boundary conditions, $$\displaylines{ (p(t)x'(t))'+ f(t,x(t))=0,\quad t\in (0,1),\cr p(0)x'(0)=p(1)x'(1),\quad x(1)=\int_0^1x(s)g(s)ds, }$$ which involves an integral boundary condition. We prove the existence of positive solutions using a new tool: the Leggett-Williams norm-type theorem for coincidences.
Classification : 34B10, 34B15, 34B45
Keywords: boundary value problem, resonance, cone, positive solution, coincidence 
@article{EJDE_2011__2011__a22,
     author = {Yang, Aijun and Sun, Bo and Ge, Weigao},
     title = {Existence of positive solutions for self-adjoint boundary-value problems with integral boundary conditions at resonance},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2011},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a22/}
}
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Yang, Aijun; Sun, Bo; Ge, Weigao. Existence of positive solutions for self-adjoint boundary-value problems with integral boundary conditions at resonance. Electronic Journal of Differential Equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a22/