On the existence and shape of least energy solutions for some elliptic systems

By A. Ávila, Jianfu Yang. 2003

75 citations recorded by the source corpus.

We establish an existence result for strongly indefinite semilinear elliptic systems with Neumann boundary condition, and we study the limiting behavior of the positive solutions of the singularly perturbed problem. (C) 2003 Elsevier Science (USA). All rights reserved.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/845f2c6d760babc0f9a54db19270e8665d520be1

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Hamiltonian elliptic systems: a guide to variational frameworks (2014, methodology): “As far as we know, the first paper to obtain concentration phenomena in Hamiltonian system is due to Ávila and Yang [11], using the dual variational formulation we presented in Section 3 (related results using this approach can be found in [3, 4]).”
Solutions with multiple spike patterns for an elliptic system (2007, background): “This difficulty was bypassed in [1, 3] by means of a dual variational formulation of the problem while in [21, 22, 24, 25] a direct approach was proposed, based on a new variational characterization of the ground-state critical levels associated to (1.”
Spike-layered solutions for an elliptic system with Neumann boundary conditions (2004, unknown): “To the best of our knowledge, the recent work [4] is the first attempt at proving that a similar phenomenon can be observed in Hamiltonian systems such as (P).”
Multiple Solutions for Asymptotically Linear Elliptic Systems (2008, background): “See, for example, Ávila and Yang [4,5], Alves, Carrião, Miyagaki [3], Yang [28] and the references therein.”