Multiple solutions for a class of bi-nonlocal problems with nonlinear Neumann boundary conditions

Ghasem A. Afrouzi; Z. Naghizadeh; Nguyen Thanh Chung

doi:10.5269/bspm.44144

Ghasem A. Afrouzi University of Mazandaran
Z. Naghizadeh University of Science and Technology of Mazandaran
Nguyen Thanh Chung Quang Binh University

Résumé

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.

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