AN EVOLUTION EQUATION WITH COMPETING p-LAPLACIAN OPERATORS

Dedicated to Professor Constantin Fetecau on the occasion of his 80th anniversary

 

Dumitru Motreanu†

Abstract: The paper investigates an initial-boundary value problem involving the competing (p, q)-Laplacian −Δp + Δq. Under some conditions, which are different from the usual ellipticity and monotonicity conditions, the existence of a generalized solution is proven through a special Galerkin approach. An example illustrates the applicability of our result.

Keywords: initial-boundary value problem, time depending competing operators, p-Laplacian, generalized solution.

MSC: 35K92, 47J35, 35K20.

DOI 10.56082/annalsarscimath.2026.4.289

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*Accepted for publication on October 07, 2026
†motreanu@univ-perp.fr, Département de Mathématiques, Université de Perpignan Via Domitia, Perpignan, 66860, France

PUBLISHED in

Annals Academy of Romanian Scientists Series on Mathematics and Its Application,

Volume 18 no 4, 2026

ISSN ONLINE 2066 – 6594
ISSN PRINT 2066 – 5997