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July/August 2018 Existence results for non-local elliptic systems with nonlinearities interacting with the spectrum
Olímpio H. Miyagaki, Fábio Pereira
Adv. Differential Equations 23(7/8): 555-580 (July/August 2018).

Abstract

In this work, we establish an existence result for a class of non-local variational elliptic systems with critical growth, but with nonlinearities interacting with the fractional laplacian spectrum. More specifically, we treat the situation when the interval defined by two eigenvalues of the real matrix coming from the linear part contains an eigenvalue of the spectrum of the fractional laplacian operator. In this case, there are situations where resonance or double resonance phenomena can occur. The novelty here is because, up to our knowledge, the results that have been appeared in the literature up to now, this interval does not intercept the fractional laplacian spectrum. The proof is made by using the linking theorem due to Rabinowitz.

Citation

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Olímpio H. Miyagaki. Fábio Pereira. "Existence results for non-local elliptic systems with nonlinearities interacting with the spectrum." Adv. Differential Equations 23 (7/8) 555 - 580, July/August 2018.

Information

Published: July/August 2018
First available in Project Euclid: 11 May 2018

zbMATH: 06889037
MathSciNet: MR3801831

Subjects:
Primary: 35B33, 35B34, 35J50, 35R11

Rights: Copyright © 2018 Khayyam Publishing, Inc.

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Vol.23 • No. 7/8 • July/August 2018
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