Electron. J. Differential Equations,
Vol. 2018 (2018), No. 74, pp. 121.
First curve of Fucik spectrum for the pfractional Laplacian
operator with nonlocal normal boundary conditions
Divya Goel, Sarika Goyal, Konijeti Sreenadh
Abstract:
In this article, we study the Fucik spectrum of the pfractional
Laplace operator with nonlocal normal derivative conditions which
is defined as the set of all
such that
has a nontrivial solution u, where
is a bounded domain in
with Lipschitz boundary,
,
,
and
.
We show existence of the first nontrivial curve
of the Fucik spectrum which is used to obtain the variational
characterization of a second eigenvalue of the problem defined above.
We also discuss some properties of this curve
,
e.g. Lipschitz continuous, strictly decreasing
and asymptotic behavior and nonresonance with respect to the
Fucik spectrum.
Submitted November 22, 2017. Published March 17, 2018.
Math Subject Classifications: 35A15, 35J92, 35J60.
Key Words: Nonlocal operator; Fucik spectrum; Steklov problem; Nonresonance.
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Divya Goel
Department of Mathematics
Indian Institute of Technology Delhi
Hauz Khas, New Delhi110016, India
email: divyagoel2511@gmail.com


Sarika Goyal
Department of Mathematics
Bennett University, Greater Noida
Uttar Pradesh  201310, India
email: sarika1.iitd@gmail.com


Konijeti Sreenadh
Department of Mathematics
Indian Institute of Technology Delhi
Hauz Khaz, New Delhi110016, India
email: sreenadh@maths.iitd.ac.in

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