Geodesic
Positive solutions for a class of nonresonant boundary-value problems
Electronic journal of differential equations, Tome 2007 (2007)
This paper concerns the existence and multiplicity of positive solutions to the nonresonant second-order boundary-value problem

$ Lx=\lambda w(t)f(t,x). $

We are interested in the operator $Lx:=-x''+\rho qx$ when $w$ is in $L^{p}$ for $1\leq p \leq +\infty$. Our arguments are based on fixed point theorems in a cone and Holder's inequality. The nonexistence of positive solutions is also studied.
Classification : 34B15
Keywords: positive solution, fixed point theorem, existence, complete continuity 
@article{EJDE_2007__2007__a55,
     author = {Zhang,  Xuemei},
     title = {Positive solutions for a class of nonresonant boundary-value problems},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1118.34020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a55/}
}
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Zhang,  Xuemei. Positive solutions for a class of nonresonant boundary-value problems. Electronic journal of differential equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a55/