Existence of solutions to biharmonic equations with sign-changing coefficients
Date
2018-04-28
Authors
Saiedinezhad, Somayeh
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we study the existence of solutions for the semi-linear elliptic equation
∆2u - α(x)∆u = b(x)|u|p-2u
with Navier boundary condition u = ∆u = 0 on ∂Ω, where Ω is a bounded domain with smooth boundary and 2 < p < 2*. We consider two different assumptions on the potentials α and b, 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.
Description
Keywords
Bi-Laplacian operator, Weak solution, Nehari manifold, Fibering map
Citation
Saiedinezhad, S. (2018). Existence of solutions to biharmonic equations with sign-changing coefficients. <i>Electronic Journal of Differential Equations, 2018</i>(99), pp. 1-9.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.