Electron. J. Diff. Equ., Vol. 2016 (2016), No. 186, pp. 1-9.

Eigenvalue estimates for stationary p(x)-Kirchhoff problems

Luca Vilasi

Using variational techniques we prove an eigenvalue theorem for a stationary p(x)-Kirchhoff problem, and provide an estimate for the range of such eigenvalues. We employ a specific family of test functions in variable-exponent Sobolev spaces. Our approach permits to handle both non-degenerate and degenerate Kirchhoff coefficients.

Submitted April 22, 2016. Published July 12, 2016.
Math Subject Classifications: 35J20, 35J62.
Key Words: Kirchhoff equation; p(x)-Laplacian; multiplicity; eigenvalue.

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Luca Vilasi
Department of Mathematical and Computer Sciences
Physical Sciences and Earth Sciences
University of Messina
Viale F. Stagno d'Alcontres
31, 98166 Messina, Italy
email: lvilasi@unime.it

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