Liouville-type results for semilinear elliptic equations in unbounded domains

By Henri Berestycki, François Hamel, Luca Rossi. 2007

155 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/467a6e2947a053ed1c8529b139fa8ef1557007b3

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Liouville Theorems for Fractional Parabolic Equations (2021, methodology): “To this end, a number of systematic approaches have been established, such as the extension method ([7]), the method of moving planes ([2, 4, 9, 10, 23]), the method of moving spheres ([11, 29]), and the sliding methods ([3, 39]).”
The principal eigenvalue of a space–time periodic parabolic operator (2009, background): “This result is a generalization of the theorem for elliptic operators that was first proved for a bounded but not necessarily smooth domain in [8] and then for general domain in [7].”
Reaction-diffusion equations for population dynamics with forced speed I - The case of the whole space (2008, methodology): “Hamel [2].”
On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators (2010, background): “6) and their properties, we follow and adapt the arguments developed in [5, 6, 20].”
Critical travelling waves for general heterogeneous one-dimensional reaction–diffusion equations (2015, background): “In particular, the results of [7] yield that the equation associated with b ≡ 0, f as in (3.”
On the definition and the properties of the principal eigenvalue of some nonlocal operators (2015, methodology): “For instance, several new notions of principal eigenvalue have been introduced for general elliptic operators defined on (limit or almost) periodic media [6, 10, 49, 56].”
Reaction-diffusionequations for population dynamics with forced speed II -cylindrical-type domains (2009, unknown): “We follow the same arguments as in the proof of Proposition 5 in [2].”
Spreading speeds for one-dimensional monostable reaction-diffusion equations (2016, background): “These quantities are involved in the statement of many properties of parabolic and elliptic equations in unbounded domains, such as maximum principles, existence and uniqueness results [7, 10, 11].”
Persistence versus extinction under a climate change in mixed environments (2014, background): “He is also thankful to Luca Rossi for many interesting discussions and proof reading.”
Spatial propagation for a two component reaction–diffusion system arising in population dynamics (2016, result): “Let us mention that similar results have been obtained by Berestycki et al in [5] for more general problems.”
Generalizations and Properties of the Principal Eigenvalue of Elliptic Operators in Unbounded Domains (2010, unknown): “The relations between 1 and 0 1 have been established in [8, 12], but only in low dimension.”