In this article, we study the existence of solutions for the semi-linear elliptic equation
with Navier boundary condition on , where is a bounded domain with smooth boundary and . We consider two different assumptions on the potentials and , including the case of sign-changing weights. The approach is based on the Nehari manifold with variational arguments about the corresponding fibering map, which ensures the multiple results.
Submitted July 17, 2017. Published Aapril 28, 2018.
Math Subject Classifications: 35A01, 35J35, 35D30, 35J91.
Key Words: Bi-Laplacian operator; weak solution; Nehari manifold; fibering map.
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| Somayeh Saiedinezhad |
School of Mathematics
Iran University of Science and Technology
Narmak, Tehran, Iran
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