Singularly perturbed elliptic equations with symmetry: Existence of solutions concentrating on spheres, part II

By A. Ambrosetti, A. Malchiodi, Wei-Ming Ni. 2004

158 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/ecd6021aab1a5f21249c919a6a86cb1326eed810

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Nonlinear schrodinger equations with unbounded and decaying radial potentials (2007, unknown): “In a recent paper [2], the authors consider −22∆u + V (|x|)u = u, x ∈ R and under the condition that a weighted potential has local maximum or local minimum they constructed radially symmetric solutions for all p > 1 as long as 2 is sufficiently small.”
Intermediate reduction method and infinitely many positive solutions of nonlinear Schrödinger equations with non-symmetric potentials (2015, background): “, curves? That is, does the Ambrosetti–Malchiodi–Ni conjecture in [3] still hold without the small parameter ε, even in the radial symmetry case? If the answer is yes, are the solutions constructed in Theorem 2.”
Semiclassical states for nonlinear Schrödinger equations with sign-changing potentials (2007, methodology): “For concentrations on higher-dimensional sets, we refer to Ambrosetti, Malchiodi and Ni [2], and M.”
Concentration phenomenon for fractional nonlinear Schr\"{o}dinger equations (2013, background): “We limit ourselves to citing a few recent papers [3, 4, 6, 7, 28, 10, 42, 53, 29], referring to their bibliography for a broader list of works, although still not exhaustive.”
Infinitely many positive solutions for the nonlinear Shcrodinger equations in $R^N$ (2008, background): “6) where ε > 0 is a small parameter, then the number of the critical points of V (y) (or Q(y)) (see for example [1, 7, 8],[13]–[16],[18, 27, 29]), the type of the critical points of V (y) (or Q(y)) (see for example [12, 21, 26], and the topology of the level set of V (y) (or Q(y)) [2, 3, 11, 19], ca”
On the number of interior peak solutions for a singularly perturbed Neumann problem (2007, unknown): “Progressin thisdirection,althoughstill limited, hasalsobeenmadein [2, 23, 24,25, 26].”
Some new entire solutions of semilinear elliptic equations on Rn (2009, background): “Existence of such solutions was shown in [3], [ 4 ], [6], [9] under some symmetry assumptions, and then in [18] the authors proved concentration along curves for n = 2 (see also [38], [39] for general n), in a non-symmetric setting.”