Differential and Integral Equations

A priori bounds and positive solutions for non-variational fractional elliptic systems

Edir Junior Ferreira Leite and Marcos Montenegro

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In this paper, we study strongly coupled elliptic systems in non-variational form involving fractional Laplace operators. We prove Liouville type theorems and, by mean of the blow-up method, we establish a priori bounds of positive solutions for subcritical and superlinear nonlinearities in a coupled sense. By using those latter, we then derive the existence of positive solutions through topological methods.

Article information

Differential Integral Equations, Volume 30, Number 11/12 (2017), 947-974.

First available in Project Euclid: 1 September 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J57: Boundary value problems for second-order elliptic systems 35J60: Nonlinear elliptic equations 35J61: Semilinear elliptic equations


Leite, Edir Junior Ferreira; Montenegro, Marcos. A priori bounds and positive solutions for non-variational fractional elliptic systems. Differential Integral Equations 30 (2017), no. 11/12, 947--974. https://projecteuclid.org/euclid.die/1504231281

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