On Positive Multipeak Solutions of a Nonlinear Elliptic Problem

By E. Noussair, Shusen Yan. 2000

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Infinitely many positive solutions for nonlinear equations with non-symmetric potentials (2012, background): “4) where ε > 0 is a small parameter and p subcritical, then the number of the critical points of V (y) (see for example [1, 36],[17]–[20],[23, 36, 45]), the type of the critical points of V (y) (see for example [8, 26, 35], and the topology of the level set of V (y) [2, 3, 9, 24], can affect the num”
Semi-Classical Bound States for Schrödinger Equations with Potentials Vanishing or Unbounded at Infinity (2009, result): “[13] Dancer, E. N., Yan, S. (2000).”
Uniqueness of positive bound states with multi-bump for nonlinear Schrödinger equations (2015, background): “For Dirichlet problems with a subcritical nonlinearity on bounded domains, the solutions concentrating at one or a couple of points were obtained in [8, 28, 29]; For the case of a critical nonlinearity, the results on the existence of multi-bump solutions can be found in [4, 34].”
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”