Geodesic
Positive solutions for singular semi-positone Neumann boundary-value problems
Electronic Journal of Differential Equations, Tome 2004 (2004).

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

Summary: In this paper, we study the singular semi-positone Neumann boundary-value problem $$\displaylines{ -u''+m^2u=\lambda f(t,u)+g(t,u),\quad 0 less than t less than 1,\cr u'(0)=u'(1)=0, }$$ where $m$ is a positive constant. Under some suitable assumptions on the functions $f$ and $g$, for sufficiently small $\lambda$, we prove the existence of a positive solution. Our approach is based on the Krasnasel'skii fixed point theorem in cones.
Classification : 34B10, 34B15
Keywords: positive solution, semi-positone, fixed points, cone, singular Neumann boundary-value problem 
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     author = {Sun, Yong-Ping and Sun, Yan},
     title = {Positive solutions for singular semi-positone {Neumann} boundary-value problems},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2004},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a161/}
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Sun, Yong-Ping; Sun, Yan. Positive solutions for singular semi-positone Neumann boundary-value problems. Electronic Journal of Differential Equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a161/