Multiplicity results for a family of semilinear elliptic problems under local superlinearity and sublinearity

de Figueiredo, Djairo Guedes, Gossez, Jean-Pierre, and Ubilla, Pedro. "Multiplicity results for a family of semilinear elliptic problems under local superlinearity and sublinearity." Journal of the European Mathematical Society 008.2 (2006): 269-288. <http://eudml.org/doc/277627>.

@article{deFigueiredo2006,
abstract = {We study the existence, nonexistence and multiplicity of positive solutions for the family of problems $−\Delta u=f_\lambda (x,u)$, $u\in H^1_0(\Omega )$, where $\Omega $ is a bounded domain in $\mathbb \{R\}^N$, $N\ge 3$ and $\lambda >0$ is a parameter. The results include the well-known nonlinearities of the Ambrosetti–Brezis–Cerami type in a more general form, namely $\lambda a(x)u^q+b(x)u^p$, where $0\le q<1<p\le 2^*−1$. The coefficient $a(x)$ is assumed to be nonnegative but $b(x)$ is allowed to change sign, even in the critical case. The notions of local superlinearity and local sublinearity introduced in [9] are essential in this more general framework. The techniques used in the proofs are lower and upper solutions and variational methods.},
author = {de Figueiredo, Djairo Guedes, Gossez, Jean-Pierre, Ubilla, Pedro},
journal = {Journal of the European Mathematical Society},
keywords = {multiplicity; semilinear elliptic problem; local sub and superlinear nonlinearities; concave-convex nonlinearities; critical exponent; upper and lower solutions; variational method; multiplicity; semilinear elliptic problem; local sub and superlinear nonlinearities; concave-convex nonlinearities; critical exponent; upper and lower solutions; variational method},
language = {eng},
number = {2},
pages = {269-288},
publisher = {European Mathematical Society Publishing House},
title = {Multiplicity results for a family of semilinear elliptic problems under local superlinearity and sublinearity},
url = {http://eudml.org/doc/277627},
volume = {008},
year = {2006},
}

TY - JOUR
AU - de Figueiredo, Djairo Guedes
AU - Gossez, Jean-Pierre
AU - Ubilla, Pedro
TI - Multiplicity results for a family of semilinear elliptic problems under local superlinearity and sublinearity
JO - Journal of the European Mathematical Society
PY - 2006
PB - European Mathematical Society Publishing House
VL - 008
IS - 2
SP - 269
EP - 288
AB - We study the existence, nonexistence and multiplicity of positive solutions for the family of problems $−\Delta u=f_\lambda (x,u)$, $u\in H^1_0(\Omega )$, where $\Omega $ is a bounded domain in $\mathbb {R}^N$, $N\ge 3$ and $\lambda >0$ is a parameter. The results include the well-known nonlinearities of the Ambrosetti–Brezis–Cerami type in a more general form, namely $\lambda a(x)u^q+b(x)u^p$, where $0\le q<1<p\le 2^*−1$. The coefficient $a(x)$ is assumed to be nonnegative but $b(x)$ is allowed to change sign, even in the critical case. The notions of local superlinearity and local sublinearity introduced in [9] are essential in this more general framework. The techniques used in the proofs are lower and upper solutions and variational methods.
LA - eng
KW - multiplicity; semilinear elliptic problem; local sub and superlinear nonlinearities; concave-convex nonlinearities; critical exponent; upper and lower solutions; variational method; multiplicity; semilinear elliptic problem; local sub and superlinear nonlinearities; concave-convex nonlinearities; critical exponent; upper and lower solutions; variational method
UR - http://eudml.org/doc/277627
ER -