Electron. J. Diff. Equ., Vol. 2014 (2014), No. 126, pp. 1-13.

Strictly positive solutions for one-dimensional nonlinear elliptic problems

Uriel Kaufmann, Ivan Medri

Abstract:
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.

Submitted June 26, 2013. Published May 14, 2014.
Math Subject Classifications: 34B15, 34B18, 35J25, 35J61.
Key Words: Elliptic one-dimensional problems; indefinite nonlinearities; sub and supersolutions; positive solutions.

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Uriel Kaufmann
FaMAF, Universidad Nacional de Córdoba, (5000)
Córdoba, Argentina
email: kaufmann@mate.uncor.edu
Iván Medri
FaMAF, Universidad Nacional de Córdoba, (5000)
Córdoba, Argentina
email: medri@mate.uncor.edu

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