Elliptic systems arise in biological applications (e.g. population dynamics) or physical applications (e.g. models of a nuclear reactor) and have been drawn a lot of attention. In the nonlocal case, there are not so many papers on weakly coupled systems in R^N. In this paper we present some recent existence, uniqueness and multiplicity results for positive solutions of a class of weakly coupled nonlocal systems of equations in R^N, which are new also in the local case. Moreover, we also provide a global compactness result, which gives a complete description of the Palais-Smale sequences of the treated systems. To the best of our knowledge, this decomposition has been studied only for systems of equations in bounded domains.
Fractional elliptic systems with critical nonlinearities
Patrizia, Pucci
2021
Abstract
Elliptic systems arise in biological applications (e.g. population dynamics) or physical applications (e.g. models of a nuclear reactor) and have been drawn a lot of attention. In the nonlocal case, there are not so many papers on weakly coupled systems in R^N. In this paper we present some recent existence, uniqueness and multiplicity results for positive solutions of a class of weakly coupled nonlocal systems of equations in R^N, which are new also in the local case. Moreover, we also provide a global compactness result, which gives a complete description of the Palais-Smale sequences of the treated systems. To the best of our knowledge, this decomposition has been studied only for systems of equations in bounded domains.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.