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3 results

Continuity of solutions for the Δϕ-Laplacian operator
Part of
Natalí A. Cantizano, Ariel M. Salort, Juan F. Spedaletti
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 151 / Issue 4 / August 2021

Published online by Cambridge University Press:

11 September 2020, pp. 1355-1382

Print publication:

August 2021
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In this paper we give sufficient conditions to obtain continuity results of solutions for the so called ϕ-Laplacian Δϕ with respect to domain perturbations. We point out that this kind of results can be extended to a more general class of operators including, for instance, nonlocal nonstandard growth type operators.

Fractional eigenvalue problems that approximate Steklov eigenvalue problems
Part of
Leandro M. Del Pezzo, Julio D. Rossi, Ariel M. Salort
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 148 / Issue 3 / June 2018

Published online by Cambridge University Press:

28 December 2017, pp. 499-516

Print publication:

June 2018
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In this paper we analyse possible extensions of the classical Steklov eigenvalue problem to the fractional setting. In particular, we find a non-local eigenvalue problem of fractional type that approximates, when taking a suitable limit, the classical Steklov eigenvalue problem.

EIGENVALUE HOMOGENISATION PROBLEM WITH INDEFINITE WEIGHTS
Part of
- Spectral theory and eigenvalue problems
- Partial differential equations
JULIÁN FERNÁNDEZ BONDER, JUAN P. PINASCO, ARIEL M. SALORT
Journal:

Bulletin of the Australian Mathematical Society / Volume 93 / Issue 1 / February 2016

Published online by Cambridge University Press:

15 October 2015, pp. 113-127

Print publication:

February 2016
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In this work we study the homogenisation problem for nonlinear elliptic equations involving $p$-Laplacian-type operators with sign-changing weights. We study the asymptotic behaviour of variational eigenvalues which consist of a double sequence of eigenvalues. We show that the $k$th positive eigenvalue goes to infinity when the average of the weights is nonpositive, and converges to the $k$th variational eigenvalue of the limit problem when the average is positive for any $k\geq 1$.