## Topological Methods in Nonlinear Analysis

### Bifurcation analysis of a singular elliptic problem modelling the equilibrium of anisotropic continuous media

#### Abstract

In this work we obtain an existence result for a class of singular quasilinear elliptic Dirichlet problems on a smooth bounded domain containing the origin. By using a Caffarelli-Kohn-Nirenberg type inequality, a critical point result for differentiable functionals is exploited, in order to prove the existence of a precise open interval of positive eigenvalues for which the treated problem admits at least one nontrivial weak solution. In the case of terms with a sublinear growth near the origin, we deduce the existence of solutions for small positive values of the parameter. Moreover, the corresponding solutions have smaller and smaller energies as the parameter goes to zero.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 45, Number 2 (2015), 493-508.

Dates
First available in Project Euclid: 30 March 2016

https://projecteuclid.org/euclid.tmna/1459343993

Digital Object Identifier
doi:10.12775/TMNA.2015.024

Mathematical Reviews number (MathSciNet)
MR3408833

Zentralblatt MATH identifier
1367.35029

#### Citation

Bisci, Giovanni Molica; Rădulescu, Vicenţiu D. Bifurcation analysis of a singular elliptic problem modelling the equilibrium of anisotropic continuous media. Topol. Methods Nonlinear Anal. 45 (2015), no. 2, 493--508. doi:10.12775/TMNA.2015.024. https://projecteuclid.org/euclid.tmna/1459343993

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