Asymptotic properties of PDEs in compact spaces

Abstract

In this article we combine the study of solutions of PDEs with the study of asymptotic properties of the solutions via compactification of the domain. We define new spaces of functions on which study the equations, prove a version of Ascoli-Arzelà Theorem, develop the fixed point index results necessary to prove existence and multiplicity of solutions in these spaces and also illustrate the applicability of the theory with an example.

References in corpus (6)

• Nonzero radial solutions for a class of elliptic systems with nonlocal BCs on annular domains
• Nonzero positive solutions of nonlocal elliptic systems with functional BCs
• Eigenvalues of elliptic functional differential systems via a Birkhoff--Kellogg type theorem
• Multiple positive radial solutions for Neumann elliptic systems with gradient dependence
• Nonzero radial solutions for elliptic systems with coupled functional BCs in exterior domains
• Positive solutions of BVPs on the half-line involving functional BCs