Open AccessMultiple solutions for a class of bi-nonlocal problems with nonlinear Neumann boundary conditions
Author(s) -
G. A. Afrouzi,
Z. Naghizadeh,
Nguyen Thanh Chung
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.44144
Subject(s) - sublinear function , mathematics , class (philosophy) , neumann boundary condition , nonlinear system , infinity , boundary value problem , boundary (topology) , mathematical analysis , von neumann architecture , pure mathematics , computer science , physics , quantum mechanics , artificial intelligence
In this paper, we are interested in a class of bi-nonlocal problems with nonlinear Neumann boundary conditions and sublinear terms at infinity. Using $(S_+)$ mapping theory and variational methods, we establish the existence of at least two non-trivial weak solutions for the problem provied that the parameters are large enough. Our result complements and improves some previous ones for the superlinear case when the Ambrosetti-Rabinowitz type conditions are imposed on the nonlinearities.