Singularly perturbed elliptic problems with superlinear or asymptotically linear nonlinearities

By Louis Jeanjean, Kazunaga Tanaka. 2004

214 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/53177701c3e5764a1befcda46b0ce8fff43f3f71

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Standing waves with a critical frequency for nonlinear Schrödinger equations, II (2003, background): “In the case inf x∈RN V> Ethe existence of a localized solution concentrating around local minimum points of V has been obtained under various conditions on general nonlinearity f (for example, in [13] and [ 23 ] and references therein).”
Spikes in Two-component Systems of Nonlinear Schrodinger Equations with Trapping Potentials (2006, background): “We refer the reader for instance to [1, 3, 2, 4, 5, 8, 9, 10, 12, 14, 15, 16, 17, 18, 22, 23, 25, 26] and the references therein.”
Existence and concentration of ground state solutions for a critical nonlocal Schr\"odinger equation in $\R^2$ (2016, methodology): “in RN, (1.2) S.S goes back to the pioneer work [24] by Floer and Weinstein. Since then, it has been studied extensively under various hypotheses on the potential and the nonlinearity, see for example [7, 16, 17, 24, 25, 26, 43, 44, 46, 48] and the references therein. In the study of semiclassical pr”
Standing Waves for Nonlinear Schrödinger Equations with a General Nonlinearity: One and Two Dimensional Cases (2008, methodology): “In a different direction, a variational approach was initiated by Rabinowitz (1992) and developed further by several authors (see Byeon and Wang, 2002, 2003; Cingolani and Lazzo, 2000; Cingolani and Nolasco, 1998; Del Pino and Felmer, 1996, 1997, 1998, 2002; Gui, 1996; Jeanjean and Tanaka, 2004).”
Concentration on curves for nonlinear Schrödinger Equations (2007, background): “We refer the reader, for instance, to [2, 4, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 22, 31, 32, 34, 36, 37, 38].”
On ground states of superlinear p-Laplacian equations in RN (2010, methodology): “In Lemma 2.3 we adopt a technique developed in [14, 16 ] and the Lions Lemma [20, Lemma I.1] to show that any Cerami sequence of Φ is bounded.”
Existence and Concentration Result for the Kirchhoff Type Equations with General Nonlinearities (2014, unknown): “Here we only refer to [5–7,17– 22,24–27,43,44,48,54,55,57,63,64] and see references therein.”
Semi-classical standing waves for nonlinear Schrödinger equations at structurally stable critical points of the potential (2013, unknown): “In the other direction, a variational approach which does not require the nondegeneracy condition for the limiting problem (4) was initiated by Rabinowitz [35] and developed further by several authors (see [10, 14, 15, 17, 23, 26]).”
Bound states for semilinear Schrödinger equations with sign-changing potential (2007, background): “We mention here the work by del Pino and Felmer [8], Ambrosetti, Malchiodi and Secchi [2], Byeon and Wang [6], Jeanjean and Tanaka [12], and Byeon and Jeanjean [5].”