该文研究如下一类临界薛定谔-泊松方程{-△u+λV(x)u+φu=μ|u|p-2u+|u|4u,x ∈R3,-△φ =u2,x ∈R3,其中λ＞0,μ＞0是两个参数,p∈(4,6),V满足一些势井条件.当参数λ充分大时,利用变分法证明了基态解的存在性,以及随着λ→∞时,这些解的渐近行为.另外,在参数λ充分大和μ充分小时,利用Ljusternik-Schnirelmann理论,到了多重解的存在性定理.
该文应用广义Laplace变换方法研究了一类广义分数阶微分系统的Hyers-Ulam-Rassias稳定性,同时给出相关例子说明了理论结果的有效性.
该文主要研究非线性项涉及局部线性增长的变指数半线性椭圆方程.利用扰动技术、变分方法和先验估计,获得了该问题正解的存在性.
A conformal restriction measure is a probability measure which is used to de-scribe the law of a random connected subset in a simply connected domain that satisfies a certain conformal restriction property.Usually there are three kinds of conformal restri
In this paper,we mainly apply a new,asymptotic method to investigate the growth of meromorphic solutions of linear higher order difference equations and differential equations.We delete the condition (1.6) of Theorems E and F,yet obtain the same results f
In this paper,we extend the concept of holomorphic curves sharing hyperplanes and introduce definitions of restricted hyperplanes and partial shared hypersurfaces.Then,we prove several normal criteria of the family of holomorphic curves and holomorphic ma
该文考虑了有界区域上一类带奇异非线性项(1-u)-2的四阶演化方程解的适定性.该模型具有很强的物理背景,它刻画了微机电模型的工作原理.首先,该文研究了四阶抛物方程解的适定性,该方程的适定性在文章[1]中通过半群理论得到验证,但是他们只限于区域空间维数为2维的情形.通过Faedo-Galerkin技巧,可以证明该方程在空间维数小于等于7的情形下解是适定的.
Assume that 0 ＜ p ＜ ∞ and that B is a connected nonempty open set in Rn,and that Ap(B) is the vector space of all holomorphic functions F in the tubular domains Rn + iB such that for any compact set K (C) B,‖y (→) ‖x (→) F(x + iy)‖Lp(Rn)‖L(K) ＜ ∞,so Ap(B)
研究n(n≥2)维分数阶扩散的MHD-Boussinesq系统.当非负常数α,β及γ满足α≥1/2+n/4,α+β≥1+n/2及α+γ≥n/2时,利用能量方法,得到了MHD-Boussinesq系统全局解的存在唯一性,推广了已有的结果.