TY  - JOUR
ID  - Goncerz2012
LB  - Goncerz2012
AU  - Goncerz, Paweł
TI  - On the existence of three solutions for quasilinear elliptic problem
ST  - On the existence of three solutions for quasilinear elliptic problem
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2012
VL  - 32
IS  - 3
SP  - 473
EP  - 486
DO  - http://dx.doi.org/10.7494/OpMath.2012.32.3.473
UR  - http://dx.doi.org/10.7494/OpMath.2012.32.3.473
AB  - We consider a quasilinear elliptic problem of the type \(-\Delta_p u = \lambda (f(u)+\mu g(u))\) in \(\Omega\), \(u|_{\partial \Omega} =0\), where \(\Omega \in \mathbb{R}^N\) is an open and bounded set, \(f\), \(g\) are continuous real functions on \(\mathbb{R}\) and \(\lambda , \mu \in \mathbb{R}\). We prove the existence of at least three solutions for this problem using the so called three critical points theorem due to Ricceri.
KW  - critical point
KW  - elliptic problem
KW  - minimax inequality
KW  - \(p\)-Laplacian
KW  - three critical points theorem
KW  - weak solution
SN  - 1232-9274
ER  -