Bifurcation analysis of a singular elliptic problem modelling the equilibrium of anisotropic continuous media
DOI:
https://doi.org/10.12775/TMNA.2015.024Keywords
Critical point theory, variational methods, Ricceri's variational principle, singular elliptic equations, bifurcation pointsAbstract
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.Downloads
Published
2015-06-01
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1.
BISCI, Giovanni Molica and RADULESCU, Vicentiu D. Bifurcation analysis of a singular elliptic problem modelling the equilibrium of anisotropic continuous media. Topological Methods in Nonlinear Analysis. Online. 1 June 2015. Vol. 45, no. 2, pp. 493 - 508. [Accessed 13 December 2024]. DOI 10.12775/TMNA.2015.024.
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