Taiwanese Journal of Mathematics

Eigenvalue Problems for Fractional $p(x,y)$-Laplacian Equations with Indefinite Weight

Nguyen Thanh Chung

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In this paper, we consider a class of eigenvalue problems for fractional $p(x,y)$-Laplacian equations with indefinite weight in fractional Sobolev space with variable exponent. Under some suitable conditions on the growth rates involved in the problem, we establish some results on the existence of a continuous family of eigenvalues using variational techniques and Ekeland's variational principle.

Article information

Taiwanese J. Math., Volume 23, Number 5 (2019), 1153-1173.

Received: 6 September 2018
Revised: 5 April 2019
Accepted: 9 April 2019
First available in Project Euclid: 23 April 2019

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Primary: 35B60: Continuation and prolongation of solutions [See also 58A15, 58A17, 58Hxx] 35J20: Variational methods for second-order elliptic equations 35J91: Semilinear elliptic equations with Laplacian, bi-Laplacian or poly- Laplacian 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems

fractional $p(x,y)$-Laplacian problems indefinite weight fractional Sobolev space variable exponent variational methods


Chung, Nguyen Thanh. Eigenvalue Problems for Fractional $p(x,y)$-Laplacian Equations with Indefinite Weight. Taiwanese J. Math. 23 (2019), no. 5, 1153--1173. doi:10.11650/tjm/190404. https://projecteuclid.org/euclid.twjm/1555984822

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