Open AccessExistence of solutions for a p-Laplacian system with a nonresonance condition between the first and the second eigenvalues
Author(s) -
Sara Dob,
Hakim Lekhal,
Messaoud Maouni
Publication year - 2022
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.49016
Subject(s) - eigenvalues and eigenvectors , p laplacian , mathematics , laplace operator , degree (music) , pure mathematics , mathematical analysis , physics , quantum mechanics , boundary value problem , acoustics
In this article, we study the existence of positive solutions for the quasilinear elliptic system −∆_p u(x) = f_1(x, v(x)) + h_1(x) in Ω,−∆_p v(x) = f_2(x, u(x)) + h_2(x) in Ω,u = v = 0 on ∂Ω,where f_i(x, s), (i = 1, 2) locates between the first and the second eigenvalues of the p-Laplacian. To prove the existence of solutions, we use a topological method the Leray-Schauder degree.