Multiplicity of asymmetric solutions for nonlinear elliptic problems

Abstract

Abstract. In this paper we study the existence of multiple asymmetric positive solutions for the following symmetric problem:

Multiple Boundary Concentrating Solutions to Dirichlet Problem of Hénon Equation

“…So, using the result in [7], we can prove that if (z, λ) ∈ B µ is a critical point of L ε (z, λ), then (3.45) holds. For the proof of (3.46), if we can prove that for i, j = 1, · · · , k, i = j, …”

Arbitrary many peak solutions for a bi-harmonic equation with nearly critical growth

“…Taking advantage of the result in [6], we can prove that if (z, λ) ∈  B µ is a critical point of L ε (z, λ), then (3.11) holds. For the proof of (3.12), if we can prove that for i, j = 1, 2, .…”

“…See, for example, [5][6][7][8][9][10][11][12] and the references therein. However, as far as the author know, the concentration phenomena for fourth order elliptic equations on bounded domain have been studied in [13][14][15][16][17][18].…”

Asymptotic profile of a least-energy solution to a nonlinear elliptic equation in nonlinear optics

“…In [10], we study (1.1) with non-autonomous nonlinearity. [4] studied (1.1) and a corresponding higher-dimensional model and obtained a two-peak solution in the one-dimensional case and a multi-peak solution which concentrates at K distinct points away from the origin as λ → ∞ for any given K in the higher-dimensional case. Their arguments are related to symmetry-breaking phenomena which appear in the Neumann problem on exterior domains (see [6,7]).…”