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

Djairo Guedes de Figueiredo; Jean-Pierre Gossez; Pedro Ubilla

Journal of the European Mathematical Society (2006)

- Volume: 008, Issue: 2, page 269-288
- ISSN: 1435-9855

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topde 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 -

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