The asymptotic behavior of constant sign and nodal solutions of (p,q)-Laplacian problems as p goes to 1

• Main Author: Figueiredo, Giovany M.
• Publication Date: 2025
• Other Authors: Pimenta, Marcos T.O. [UNESP], Winkert, Patrick
• Format: Article
• Language: eng
• Source: Repositório Institucional da UNESP
• Download full: http://dx.doi.org/10.1016/j.na.2024.113677; https://hdl.handle.net/11449/297339
• topic: 1-laplacian; Asymptotic behavior; Functions of bounded variation; p goes to 1; Sign-changing solutions

In this paper we study the asymptotic behavior of solutions to the (p,q)-equation [Formula presented]has at least two constant sign solutions and one sign-changing solution, whereby the sign-changing solution has least energy among all sign-changing solutions. Furthermore, the solutions belong to the usual Sobolev space W01,q(Ω) which is in contrast with the case of 1-Laplacian problems, where the solutions just belong to the space BV(Ω) of all functions of bounded variation. As far as we know this is the first work dealing with (1,q)-Laplace problems even in the direction of constant sign solutions.