Existence of solutions for a p-Laplacian system with a nonresonance condition between the first and the second eigenvalues | Zendy

Sara Dob | Zendy; Hakim Lekhal | Zendy; Messaoud Maouni | Zendy

Open Access

Existence 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.

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