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Ground State of N Coupled Nonlinear Schrödinger Equations in Rn,n≤3
We establish some general theorems for the existence and nonexistence of ground state solutions of steady-state N coupled nonlinear Schrödinger equations. The sign of coupling constants βij’s isExpand
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On a two-dimensional elliptic problem with large exponent in nonlinearity
A semilinear elliptic equation on a bounded domain in R2 with large exponent in the nonlinear term is studied in this paper. We investigate positive solutions obtained by the variational method. ItExpand
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Spikes in two coupled nonlinear Schrödinger equations
Here we study the interaction and the configuration of spikes in a double condensate by analyzing least energy solutions of two coupled nonlinear Schrodinger equations which model Bose–EinsteinExpand
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The stability of spike solutions to the one-dimensional Gierer—Meinhardt model
Abstract The stability properties of an N-spike equilibrium solution to a simplified form of the Gierer–Meinhardt activator–inhibitor model in a one-dimensional domain is studied asymptotically inExpand
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On Single Interior Spike Solutions Of Gierer-Meinhardt System: Uniqueness And Spectrum Estimates
  • J. Wei
  • Mathematics
  • 1 August 1999
We study the interior spike solutions to a steady state problem of the shadow system of the Gierer–Meinhardt system arising from biological pattern formation. We first show that at a non-degenerateExpand
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Asymptotic behavior of a nonlinear fourth order eigenvalue problem
  • J. Wei
  • Mathematics
  • 31 December 1996
Our purpose in this paper is to study the asymptotic behavior of the nonlinear eigenvalue problem, where {Omega} is a smooth bounded domain in R{sup 4}, {line_integral}(u) is an nonnegative smoothExpand
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Self-similar solutions for the anisotropic affine curve shortening problem
Abstract. Similarity between the roles of the group $SL(2,\bf R)$ on the equation for self-similar solutions of the anisotropic affine curve shortening problem and of the conformal group of $S^2$ onExpand
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Concentration on curves for nonlinear Schrödinger Equations
We consider the problem where p > 1, e > 0 is a small parameter, and V is a uniformly positive, smooth potential. Let Γ be a closed curve, nondegenerate geodesic relative to theExpand
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Convergence for a Liouville equation
Abstract. In this paper, we study the asymptotic behavior of solutions of the Dirichlet problem for the Liouville equation ¶¶ $ -\Delta u= \lambda {{K(x)e^u} \over {\int_{\Omega}K(x)e^u}} $¶¶on aExpand
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Spikes in Two-component Systems of Nonlinear Schrodinger Equations with Trapping Potentials
Abstract Recently, two-component systems of nonlinear Schrodinger equations with trap potentials have been well-known to describe a binary mixture of Bose–Einstein condensates called a doubleExpand
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