Topological Methods in Nonlinear Analysis

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

Giovanni Molica Bisci and Vicenţiu D. Rădulescu

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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.

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

First available in Project Euclid: 30 March 2016

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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.

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