Existence of solutions for a nonhomogeneous elliptic Kircchoff type equation

Author(s)

Arcoya, David ^[1] ; de Paiva, Francisco Odair ^[2] ; Mendoza, Jose M. ^[3]

Affiliation

^[1] Univ Granada, Dept Math Anal, E-18071 Granada - Spain

^[2] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP - Brazil

^[3] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: Journal of Mathematical Analysis and Applications; v. 480, n. 2 DEC 15 2019.
• Web of Science Citations: 0

Abstract

For a bounded domain Omega in R-N, a bounded Caratheodory function g in Omega x R, and a nonnegative and nonzero locally integrable measurable function h in Omega, we give sufficient conditions on the C-1-function M : {[}0, infinity) -> R for the existence of a solution of the nonlocal elliptic problem [ -(1 + gamma M' (integral(Omega )vertical bar del u vertical bar(2)))Delta u = lambda u +g(x,u) - h(x)vertical bar u vertical bar(p-1)u+f(x), x is an element of Omega u(x) = 0, x is an element of partial derivative Omega for every p > 1, gamma > 0, lambda is an element of R and f is an element of L-2 (Omega). (C) 2019 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 17/16108-6 - Elliptic problems by variational and topological methods
• Grantee: Francisco Odair Vieira de Paiva
• Support Opportunities: Regular Research Grants
• FAPESP's process: 18/12881-5 - Locally coercive elliptic problems.
• Grantee: Jose Miguel Mendoza Aranda
• Support Opportunities: Scholarships in Brazil - Post-Doctoral