EXISTENCE, NONEXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS FOR THE POLY-LAPLACIAN AND NONLINEARITIES WITH ZEROS

Autor(es)

Iturriaga, Leonelo ^[1] ; Massa, Eugenio ^[2]

Afiliação do(s) autor(es)

^[1] Univ Tecn Federico Santa Maria, Dept Matemat, Ave Esparia 1680, Casilla 110-V, Valparaiso - Chile

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat, Campus Sao Carlos, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 38, n. 8, p. 3831-3850, AUG 2018.
• Citações Web of Science: 0

Resumo

In this paper we consider the equation (-Delta)(k) u = lambda f(x,u) + mu g(x,u) with Navier boundary conditions, in a bounded and smooth domain. The main interest is when the nonlinearity is nonnegative but admits a zero and f, g are, respectively, identically zero above and below the zero. We prove the existence of multiple positive solutions when the parameters lie in a region of the form lambda > (lambda) over bar and 0 < mu < (mu) over bar(lambda), then we provide further conditions under which, respectively, the bound (mu) over bar(lambda) is either necessary, or can be removed. (AU)

• Processo FAPESP: 14/25398-0 - Equações e sistemas elípticos com vários tipos de interação com o espectro
• Beneficiário: Eugenio Tommaso Massa
• Modalidade de apoio: Auxílio à Pesquisa - Regular