In this paper we consider exact solutions to the KdV equation under the Bargmann constraint. Solutions expressed through exponential polynomials and Wronskians are derived by bilinear approach through solving the Lax ...In this paper we consider exact solutions to the KdV equation under the Bargmann constraint. Solutions expressed through exponential polynomials and Wronskians are derived by bilinear approach through solving the Lax pair under the Bargmann constraint. It is also shown that the potential u in the stationary Sehrodinger equation can be a summation of squares of wave functions from bilinear point of view.展开更多
Abstract： Let Ω belong to R^N be a smooth bounded domain such that 0 ∈ Ω, N ≥ 5, 2^＊ ：2N/N-4 is the critical Sobolev exponent, and f（x） is a given function. By using the variational methods, the paper proves ...Abstract： Let Ω belong to R^N be a smooth bounded domain such that 0 ∈ Ω, N ≥ 5, 2^＊ ：2N/N-4 is the critical Sobolev exponent, and f（x） is a given function. By using the variational methods, the paper proves the existence of solutions for the singular critical in the homogeneous problem △^u-μ u/{x}^4=｜μ｜^2＊-2u＋f（x） with Dirichlet boundary condition on 偏dΩ under some assumptions on f（x） and μ.展开更多
基金Supported by National Natural Science Foundation of China under Grant Nos. 10871165 and 10671121
文摘In this paper we consider exact solutions to the KdV equation under the Bargmann constraint. Solutions expressed through exponential polynomials and Wronskians are derived by bilinear approach through solving the Lax pair under the Bargmann constraint. It is also shown that the potential u in the stationary Sehrodinger equation can be a summation of squares of wave functions from bilinear point of view.
文摘Abstract： Let Ω belong to R^N be a smooth bounded domain such that 0 ∈ Ω, N ≥ 5, 2^＊ ：2N/N-4 is the critical Sobolev exponent, and f（x） is a given function. By using the variational methods, the paper proves the existence of solutions for the singular critical in the homogeneous problem △^u-μ u/{x}^4=｜μ｜^2＊-2u＋f（x） with Dirichlet boundary condition on 偏dΩ under some assumptions on f（x） and μ.
