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)
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},
     year = {2011},
     volume = {2011},
     zbl = {1211.34031},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a22/}
}
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AU  - Sun,  Bo
AU  - Ge,  Weigao
TI  - Existence of positive solutions for self-adjoint boundary-value problems with integral boundary conditions at resonance
JO  - Electronic journal of differential equations
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VL  - 2011
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%A Sun,  Bo
%A Ge,  Weigao
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%J Electronic journal of differential equations
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%F EJDE_2011__2011__a22
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/