On the spectrum of a fourth order nonlinear eigenvalue problem with variable exponent and indefinite potential

The present paper deals with the spectrum of a fourth order nonlinear eigenvalue problem involving variable exponent conditions and a sign-changing potential. The main result of this paper establishes the existence of two positive constants $\lambda_0$ and $\lambda_1$ with $\lambda_0\leq \lambda_1$...

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Bibliographic Details
Published in:Electronic journal of qualitative theory of differential equations 2016-01, Vol.2016 (58), p.1-14
Main Authors: Zhou, Qing-Mei, Wang, Ke-Qi
Format: Article
Language:English
Subjects:
eigenvalue problem
fourth order elliptic equation
indefinite potential
variable exponent
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Summary:The present paper deals with the spectrum of a fourth order nonlinear eigenvalue problem involving variable exponent conditions and a sign-changing potential. The main result of this paper establishes the existence of two positive constants $\lambda_0$ and $\lambda_1$ with $\lambda_0\leq \lambda_1$ such that every $\lambda\in [\lambda_1, +\infty)$ is an eigenvalue, while $\lambda\in (-\infty,\lambda_0)$ cannot be an eigenvalue of the above problem.
ISSN:1417-3875
1417-3875
DOI:10.14232/ejqtde.2016.1.58