Work

Bifurcation results and multiple solutions for the fractional (p, q)-Laplace operators

Year: 2026

Type: article

Abstract: We investigate a nonlinear nonlocal eigenvalue problem involving the fractional ( p , q )-Laplace operators $$(-\Delta )_p^{s_1}+(-\Delta )_q^{s_2}$$ ( - Δ ) p s 1 + ( - Δ ) q s 2 with $$s_1,s_2\in (0,1)$$ s 1 , s 2 ∈ ( 0 , 1 ) ; $$p,q\in (1,\infty )$$ p , q ∈ ( 1 , ∞ ) and subject to Dirichlet boundary conditions in an open bounded set of $$\mathbb {R}^N$$ R N . We prove bifurcation results from trivial solutions and from infinity for the considered nonlinear nonlocal eigenvalue problem, and show the existence of multiple solutions of the nonlinear nonlocal problem using variational methods and some topological techniques.

Source: Fractional Calculus and Applied Analysis

DOI: 10.1007/s13540-026-00489-7

Authors: Emmanuel Wend-Benedo Zongo, Pierre Aime Feulefack

Institutions: Université de Toulouse, Institut de Mathématiques de Toulouse, University of Pennsylvania

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,590

Funders: Agence Nationale de la Recherche, Université Toulouse III - Paul Sabatier