EXISTENCE AND MULTIPLICITY FOR FRACTIONAL DIRICHLET PROBLEM WITH γ(ξ)-LAPLACIAN EQUATION AND NEHARI MANIFOLD

This paper is divided in two parts. In the first part, we prove coercivity results and minimization of the Euler energy functional. In the second part, we focus on the existence and multiplicity of a positive solution of fractional Dirichlet problem involving the γ(ξ)-Laplacian equation with non-neg...

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Published inApplicable analysis and discrete mathematics Vol. 17; no. 2; pp. 480 - 495
Main Authors da C. Sousa, J. Vanterler, Oliveira, D. S., Agarwal, Ravi P.
Format Journal Article
LanguageEnglish
Published University of Belgrade, Serbia 01.10.2023
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ISSN1452-8630
2406-100X
DOI10.2298/AADM220903017S

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Summary:This paper is divided in two parts. In the first part, we prove coercivity results and minimization of the Euler energy functional. In the second part, we focus on the existence and multiplicity of a positive solution of fractional Dirichlet problem involving the γ(ξ)-Laplacian equation with non-negative weight functions in H γ ( ξ ) α , β ; X ( Λ , ℝ ) using some variational techniques and Nehari manifold.
ISSN:1452-8630
2406-100X
DOI:10.2298/AADM220903017S