Geodesic
Strictly positive solutions for one-dimensional nonlinear elliptic problems
Electronic Journal of Differential Equations, Tome 2014 (2014).

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

Summary: We study the existence and nonexistence of strictly positive solutions for the elliptic problems $Lu=m(x) u^p$ in a bounded open interval, with zero boundary conditions, where $L$ is a strongly uniformly elliptic differential operator, $p\in(0,1)$, and $m$ is a function that changes sign. We also characterize the set of values $p$ for which the problem admits a solution, and in addition an existence result for other nonlinearities is presented.
Classification : 34B15, 34B18, 35J25, 35J61
Keywords: elliptic one-dimensional problems, indefinite nonlinearities, sub and supersolutions, positive solutions 
@article{EJDE_2014__2014__a135,
     author = {Kaufmann, Uriel and Medri, Iv\'an},
     title = {Strictly positive solutions for one-dimensional nonlinear elliptic problems},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2014},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a135/}
}
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Kaufmann, Uriel; Medri, Iván. Strictly positive solutions for one-dimensional nonlinear elliptic problems. Electronic Journal of Differential Equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a135/