Advances in Differential Equations

Existence results for non-local elliptic systems with nonlinearities interacting with the spectrum

Olímpio H. Miyagaki and Fábio Pereira

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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.

Article information

Adv. Differential Equations, Volume 23, Number 7/8 (2018), 555-580.

First available in Project Euclid: 11 May 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35R11: Fractional partial differential equations 35B33: Critical exponents 35J50: Variational methods for elliptic systems 35B34: Resonances


Miyagaki, Olímpio H.; Pereira, Fábio. Existence results for non-local elliptic systems with nonlinearities interacting with the spectrum. Adv. Differential Equations 23 (2018), no. 7/8, 555--580.

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