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Indexed by:Journal Papers

Date of Publication:2020-02-01

Journal:NONLINEARITY

Included Journals:SCIE

Volume:33

Issue:2

Page Number:762-789

ISSN No.:0951-7715

Key Words:Lane-Emden system; Sobolev hyperbola; periodic solutions

Abstract:Consider the periodic parabolic Lane-Emden type system , in a bounded domain of with periodic coefficients and , subject to homogeneous Dirichlet boundary condition. It is known that for the elliptic system , in the 3-dimensional (3D) space, there exists a Sobolev hyperbola , which characterizes the existence and nonexistence of nontrivial solutions. In this paper, we show that such a Sobolev hyperbola is also critical to the existence of periodic solutions for the periodic Lane-Emden type system. Moreover, different from the elliptic system, there exists another cure pq = 1, which is singular for the existence of periodic solutions.