Geodesic
Positive solutions for a class of nonresonant boundary-value problems
Electronic Journal of Differential Equations, Tome 2007 (2007).

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

Summary: 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 
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     author = {Zhang, Xuemei},
     title = {Positive solutions for a class of nonresonant boundary-value problems},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2007},
     year = {2007},
     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/