Semilinear Neumann boundary value problems on a rectangle

By Junping Shi. 2002

66 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/733056604d9ab7afb7596657ef4174ba81c0194c

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Global Bifurcation and Structure of Turing Patterns in the 1-D Lengyel–Epstein Model (2004, methodology): “For a simple evaluation of this integral we shall apply several change of variables to transform it into a regular one, following the original idea of Opial [16] (see also [18, 19 ] for advanced approach).”
Multidimensional boundary layers for a singularly perturbed Neumann problem (2004, background): “However, since the Morse index of the solutions is still changing with ε, bifurcation of non-symmetric solutions occurs from the branch of the symmetric ones, see [4], [15], [42].”
Concentration at curves for a singularly perturbed Neumann problem in three-dimensional domains (2005, background): “It is also proved that, besides these radial solutions, bifurcation of non-radial solutions occurs as an efiect of the underlying resonance phenomenon, see also [7], [ 38 ].”
Singularly Perturbed Elliptic Equations with Symmetry: Existence of Solutions Concentrating on Spheres, Part I (2003, background): “The latter question has been investigated in [13] for a somewhat related problem, see also [ 35 ].”
Dynamics and pattern formation in a diffusive predator–prey system with strong Allee effect in prey (2011, unknown): “Note that (f2) in [46] is not necessary, but only for definiteness, see remark on p.”
Existence and non-existence of spatial patterns in a ratio-dependent predator–prey model (2015, unknown): “…criteria for the stability of homogeneous steady-state and derivation of appropriate conditions for the existence and/or non-existence of non-constant stationary states (Pang and Wang, 2003; Peng and Shi, 2009; Peng et al., 2008; Shi, 2002; Shi et al., 2010; Smoller, 1994; Wang et al., 2011).”
Some new entire solutions of semilinear elliptic equations on Rn (2009, result): “We also refer to the papers [45], [50], [57] for related results.”