共查询到20条相似文献,搜索用时 31 毫秒
1.
Given a continuous strictly monotone function \(\varphi \) defined on an open real interval I and a probability measure \(\mu \) on the Borel subsets of [0, 1], the Makó–Páles mean is defined by Under some conditions on the functions \(\varphi \) and \(\psi \) defined on I, the quotient mean is given by In this paper, we study some invariance of the quotient mean with respect to Makó–Páles means.
相似文献
$$\begin{aligned} {\mathcal {M}}_{\varphi ,\mu }(x,y):=\varphi ^{-1}\left( \int ^1_0\varphi (tx+(1-t)y)\, d\mu (t)\right) ,\quad x,y\in I. \end{aligned}$$
$$\begin{aligned} Q_{\varphi ,\psi }(x,y):=\left( \frac{\varphi }{\psi }\right) ^{-1}\left( \frac{\varphi (x)}{\psi (y)}\right) , \quad x,y\in I. \end{aligned}$$
2.
In this article, we study the existence of infinitelymany solutions for the boundary–value problem , where Ω is a bounded domain with smooth boundary in ? N (N ≥ 2) and Δγ is a subelliptic operator of the form . Our main tools are the local linking and the symmetric mountain pass theorem in critical point theory.
相似文献
$$ - {\Delta _\gamma }u + a\left( x \right)u = f\left( {x,u} \right)in\Omega ,u = 0on\partial \Omega $$
$${\Delta _\gamma }: = \sum\limits_{j = 1}^N {{\partial _{{x_j}}}\left( {\gamma _j^2{\partial _{{x_j}}}} \right)} ,{\partial _{{x_j}}}: = \frac{\partial }{{\partial {x_j}}},\gamma = \left( {{\gamma _1},{\gamma _2}, \cdots ,\gamma N} \right)$$
3.
The so-called generalized associativity functional equation has been investigated under various assumptions, for instance when the unknown functions G, H, J, and K are real, continuous, and strictly monotonic in each variable. In this note we investigate the following related problem: given the functions J and K, find every function F that can be written in the form for some functions G and H. We show how this problem can be solved when any of the inner functions J and K has the same range as one of its sections.
相似文献
$$\begin{aligned} G(J(x,y),z) = H(x,K(y,z)) \end{aligned}$$
$$\begin{aligned} F(x,y,z) = G(J(x,y),z) = H(x,K(y,z)) \end{aligned}$$
4.
We prove the local boundedness of variational solutions and parabolic minimizers to evolutionary problems, where the integrand f is convex and satisfies a non-standard p, q-growth condition withA function \({u\colon \Omega_T := \Omega \times (0,T) \to \mathbb{R}}\) is called parabolic minimizer if it satisfies the minimality conditionfor every \({\varphi \in C^\infty_0(\Omega_T)}\). Moreover, we will show local boundedness for parabolic minimizers, if f satisfies an anisotropic growth condition.
相似文献
$$1 < p \leq q \leq p \tfrac{n+2}{n}.$$
$$\int_{\Omega_T} u \cdot \partial_t \varphi +f(x, Du) {\rm d} z \leq \int_{\Omega_T} f(x, Du + D \varphi) {\rm d}z$$
5.
Ran Zhuo 《中国科学 数学(英文版)》2017,60(3):491-510
We study positive solutions of the following polyharmonic equation with Hardy weights associated to Navier boundary conditions on a half space:?????(-?)~mu(x)=u~p(x)/|x|~s,in R_+~n,u(x)=-?u(x)=…=(-?)~(m-1)u(x)=0,on ?R_+~n,(0.1)where m is any positive integer satisfying 02mn.We first prove that the positive solutions of(0.1)are super polyharmonic,i.e.,(-?)~iu0,i=0,1,...,m-1.(0.2) For α=2m,applying this important property,we establish the equivalence between (0.1) and the integral equation u(x)=c_n∫R_+~n(1/|x-y|~(n-α)-1/|x~*-y|~(n-α))u~p(y)/|y|~sdy,(0.3) where x~*=(x1,...,x_(n-1),-x_n) is the reflection of the point x about the plane R~(n-1).Then,we use the method of moving planes in integral forms to derive rotational symmetry and monotonicity for the positive solution of(0.3),in whichαcan be any real number between 0 and n.By some Pohozaev type identities in integral forms,we prove a Liouville type theorem—the non-existence of positive solutions for(0.1). 相似文献
6.
We use bounds of mixed character sums modulo a square-free integer q of a special structure to estimate the density of integer points on the hypersurface for some polynomials \(f_i \in {\mathbb {Z}}[X]\) and nonzero integers a and \(k_i\), \(i=1, \ldots , n\). In the case of the above hypersurface is known as the Markoff–Hurwitz hypersurface, while for it is known as the Dwork hypersurface. Our results are substantially stronger than those known for general hypersurfaces.
相似文献
$$\begin{aligned} f_1(x_1) + \cdots + f_n(x_n) =a x_1^{k_1} \ldots x_n^{k_n} \end{aligned}$$
$$\begin{aligned} f_1(X) = \cdots = f_n(X) = X^2\quad \text{ and }\quad k_1 = \cdots = k_n =1 \end{aligned}$$
$$\begin{aligned} f_1(X) = \cdots = f_n(X) = X^n\quad \text{ and }\quad k_1 = \cdots = k_n =1 \end{aligned}$$
7.
Chen Zou 《应用数学学报(英文版)》2016,32(4):813-832
The bipolar non-isentropic compressible Navier-Stokes-Poisson (BNSP) system is investigated in R3 in the present paper, and the optimal L 2 time decay rate for the global classical solution is established. It is shown that the total densities, total momenta and total temperatures of two carriers converge to the equilibrium states at the rate in L 2-norm for any small and fix ε > 0. But, both the difference of densities and the difference of temperatures of two carriers decay at the optimal rate , and the difference of momenta decays at the optimal rate . This phenomenon on the charge transport shows the essential difference between the non-isentropic unipolar NSP and the bipolar NSP system.
相似文献
$${\left( {1 + t} \right)^{ - \frac{3}{4} + \varepsilon }}$$
$${\left( {1 + t} \right)^{ - \frac{3}{4}}}$$
$${\left( {1 + t} \right)^{ - \frac{1}{4}}}$$
8.
We find conditions under which the system of root functions of the operator is a Riesz basis in L 2[0, 1].
相似文献
$$L_y = l[y] = ay'(x) + y'(1 - x) + p_1 (x)y(x) + p_2 (x)y(1 - x),x \in [0,1],U_1 (y) = \int\limits_0^1 {y(t)d\sigma (t) = 0,} $$
9.
Rodolfo Collegari Márcia Federson Miguel Frasson 《Czechoslovak Mathematical Journal》2018,68(4):889-920
We present a variation-of-constants formula for functional differential equations of the form , where \(\mathcal{L}\) is a bounded linear operator and φ is a regulated function. Unlike the result by G. Shanholt (1972), where the functions involved are continuous, the novelty here is that the application t \(t \mapsto f\left( {y_t,t} \right)\) is Kurzweil integrable with t in an interval of ?, for each regulated function y. This means that t \(t \mapsto f\left( {y_t,t} \right)\) may admit not only many discontinuities, but it can also be highly oscillating and yet, we are able to obtain a variation-of-constants formula. Our main goal is achieved via theory of generalized ordinary differential equations introduced by J.Kurzweil (1957). As a matter of fact, we establish a variation-of-constants formula for general linear generalized ordinary differential equations in Banach spaces where the functions involved are Kurzweil integrable. We start by establishing a relation between the solutions of the Cauchy problem for a linear generalized ODE of type and the solutions of the perturbed Cauchy problem Then we prove that there exists a one-to-one correspondence between a certain class of linear generalized ODE and the Cauchy problem for a linear functional differential equations of the form , where \(\mathcal{L}\) is a bounded linear operator and φ is a regulated function. The main result comes as a consequence of such results. Finally, because of the extent of generalized ODEs, we are also able to describe the variation-of-constants formula for both impulsive FDEs and measure neutral FDEs.
相似文献
$$\dot y = \mathcal{L}\left( t \right)y_t + f\left( {y_t,t} \right),\;y_{t_0}= \varphi $$
$$\frac{{dx}}{{d\tau }} = D\left[ {A\left( t \right)x} \right],x\left( {{t_0}} \right) = \tilde x$$
$$\frac{{dx}}{{d\tau }} = D\left[ {A\left( t \right)x + F\left( {x,t} \right)} \right],x\left( {{t_0}} \right) = \tilde x$$
$$\dot y = \mathcal{L}\left( t \right)y_t,\;y_{t_0} = \varphi$$
10.
E. I. Abduragimov 《Russian Mathematics (Iz VUZ)》2008,52(12):1-3
We consider the Dirichlet problem for the nonlinear differential equation with constant m ≥ 0 and p > 1 in the unit ball S = {x ∈ R n : |x| < 1}(n ≥ 3) with the boundary Γ. We prove that with p ≤ m+n/n?2 this problem has a unique positive radially symmetric solution.
相似文献
$u_\Gamma = 0$
$\Delta u + \left| x \right|^m \left| u \right|^p = 0, x \in S,$
11.
Analytic Hypoellipticity for a New Class of Sums of Squares of Vector Fields in $${\mathcal {R}}^3$$
David S. Tartakoff 《Journal of Geometric Analysis》2017,27(2):1237-1259
This paper is devoted to a substantial generalization of previous work on the analytic hypoellipticity of sums of squares \(P=\sum _1^4X^2_j\) of real vector fields with real analytic coefficient in three variables. For p(x, y) quasi-homogeneous in (x, y), consider the vector fields \( n_1, n_2 \ne 0\). We show that the operator well known to be \(C^\infty \)-hypoelliptic, is actually analytic hypoelliptic near the origin in \({\mathcal {R}}^3\).
相似文献
$$\begin{aligned} X_1 = \frac{\partial }{\partial x}, \quad X_2=-\frac{\partial }{\partial y} + p(x,y)\frac{\partial }{\partial t}, \quad X_3=x^{n_1}\frac{\partial }{\partial t}, \quad X_4=y^{n_2}\frac{\partial }{\partial t}, \end{aligned}$$
$$\begin{aligned} P=\sum _1^4 X_j^2, \end{aligned}$$
12.
Ri-An Yan Shu-Rong Sun Dian-Wu Yang 《Journal of Applied Mathematics and Computing》2015,48(1-2):187-203
In this paper, we study the existence of solutions for the boundary value problems of fractional perturbation differential equations or subject to where \(1<\alpha <2,\,D^{\alpha }\) is the standard Caputo fractional derivatives. Using some fixed point theorems, we prove the existence of solutions to the two types. For each type we give an example to illustrate our results.
相似文献
$$\begin{aligned} D^{\alpha }\left( \frac{x(t)}{f(t,x(t))}\right) =g(t,x(t)),\;\;a.e.\;t\in J=[0,1], \end{aligned}$$
$$\begin{aligned} D^{\alpha }\left( x(t)-f(t,x(t))\right) =g(t,x(t)),\;\;a.e.\;t\in J, \end{aligned}$$
$$\begin{aligned} x(0)=y(x),\;\;x(1)=m, \end{aligned}$$
13.
Qingfeng Sun 《The Ramanujan Journal》2017,44(1):13-36
Let f be a cuspidal newform (holomorphic or Maass) of arbitrary level and nebentypus and denote by \(\lambda _f(n)\) its nth Hecke eigenvalue. Let In this paper, we study the shifted convolution sum and establish uniform bounds with respect to the shift h for \(\mathcal {S}_h(X)\).
相似文献
$$\begin{aligned} r(n)=\#\left\{ (n_1,n_2)\in \mathbb {Z}^2:n_1^2+n_2^2=n\right\} . \end{aligned}$$
$$\begin{aligned} \mathcal {S}_h(X)=\sum _{n\le X}\lambda _f(n+h)r(n), \qquad 1\le h\le X, \end{aligned}$$
14.
In this paper, we mainly consider the initial boundary problem for a quasilinear parabolic equation u_t-div(|?u|~(p-2)?u) =-|u|~(β-1) u + α|u|~(q-2 )u,where p 1, β 0, q≥1 and α 0. By using Gagliardo-Nirenberg type inequality, the energy method and comparison principle, the phenomena of blowup and extinction are classified completely in the different ranges of reaction exponents. 相似文献
15.
For \(k,l\in \mathbf {N}\), let We prove that the inequality is valid for all natural numbers k and l. The sign of equality holds if and only if \(k=l=1\). This complements a result of Vietoris, who showed that An immediate corollary is that The constant bounds are sharp.
相似文献
$$\begin{aligned}&P_{k,l}=\Bigl (\frac{l}{k+l}\Bigr )^{k+l} \sum _{\nu =0}^{k-1} {k+l\atopwithdelims ()\nu } \Bigl (\frac{k}{l}\Bigr )^{\nu }\\&\quad \text{ and }\quad Q_{k,l}=\Bigl (\frac{l}{k+l}\Bigr )^{k+l} \sum _{\nu =0}^{k} {k+l\atopwithdelims ()\nu } \Bigl (\frac{k}{l}\Bigr )^{\nu }. \end{aligned}$$
$$\begin{aligned} \frac{1}{4}\le P_{k,l} \end{aligned}$$
$$\begin{aligned} P_{k,l}<\frac{1}{2} \quad {(k,l\in \mathbf {N})}. \end{aligned}$$
$$\begin{aligned} \frac{1}{4}\le P_{k,l}<\frac{1}{2} <Q_{k,l}\le \frac{3}{4} \quad {(k,l\in \mathbf {N})}. \end{aligned}$$
16.
Esteban Andruchow 《Complex Analysis and Operator Theory》2016,10(6):1383-1409
An idempotent operator E in a Hilbert space \({\mathcal {H}}\) \((E^2=1)\) is written as a \(2\times 2\) matrix in terms of the orthogonal decomposition (R(E) is the range of E) as We study the sets of idempotents that one obtains when \(E_{1,2}:R(E)^\perp \rightarrow R(E)\) is a special type of operator: compact, Fredholm and injective with dense range, among others.
相似文献
$$\begin{aligned} {\mathcal {H}}=R(E)\oplus R(E)^\perp \end{aligned}$$
$$\begin{aligned} E=\left( \begin{array}{l@{\quad }l} 1_{R(E)} &{} E_{1,2} \\ 0 &{} 0 \end{array} \right) . \end{aligned}$$
17.
We prove the existence of infinitely many solutions for where V(x) satisfies \(\lim _{|x| \rightarrow \infty } V(x) = V_\infty >0\) and some conditions. We require conditions on f(u) only around 0 and at \(\infty \).
相似文献
$$\begin{aligned} - \Delta u + V(x) u = f(u) \quad \text { in } \mathbb {R}^N, \quad u \in H^1(\mathbb {R}^N), \end{aligned}$$
18.
Silvia Cingolani Louis Jeanjean Kazunaga Tanaka 《Journal of Fixed Point Theory and Applications》2017,19(1):37-66
We study, in the semiclassical limit, the singularly perturbed nonlinear Schrödinger equations where \(N \ge 3\), \(L^{\hbar }_{A,V}\) is the Schrödinger operator with a magnetic field having source in a \(C^1\) vector potential A and a scalar continuous (electric) potential V defined by Here, f is a nonlinear term which satisfies the so-called Berestycki-Lions conditions. We assume that there exists a bounded domain \(\Omega \subset \mathbb {R}^N\) such that and we set \(K = \{ x \in \Omega \ | \ V(x) = m_0\}\). For \(\hbar >0\) small we prove the existence of at least \({\mathrm{cupl}}(K) + 1\) geometrically distinct, complex-valued solutions to (0.1) whose moduli concentrate around K as \(\hbar \rightarrow 0\).
相似文献
$$\begin{aligned} L^{\hbar }_{A,V} u = f(|u|^2)u \quad \hbox {in}\quad \mathbb {R}^N \end{aligned}$$
(0.1)
$$\begin{aligned} L^{\hbar }_{A,V}= -\hbar ^2 \Delta -\frac{2\hbar }{i} A \cdot \nabla + |A|^2- \frac{\hbar }{i}\mathrm{div}A + V(x). \end{aligned}$$
(0.2)
$$\begin{aligned} m_0 \equiv \inf _{x \in \Omega } V(x) < \inf _{x \in \partial \Omega } V(x) \end{aligned}$$
19.
In this paper we consider the random r-uniform r-partite hypergraph model H(n 1, n 2, ···, n r; n, p) which consists of all the r-uniform r-partite hypergraphs with vertex partition {V 1, V 2, ···, V r} where |V i| = n i = n i(n) (1 ≤ i ≤ r) are positive integer-valued functions on n with n 1 +n 2 +···+n r = n, and each r-subset containing exactly one element in V i (1 ≤ i ≤ r) is chosen to be a hyperedge of H p ∈ H (n 1, n 2, ···, n r; n, p) with probability p = p(n), all choices being independent. Let and be the maximum and minimum degree of vertices in V 1 of H, respectively; , be the number of vertices in V 1 of H with degree d, at least d, at most d, and between c and d, respectively. In this paper we obtain that in the space H(n 1, n 2, ···, n r; n, p), all have asymptotically Poisson distributions. We also answer the following two questions. What is the range of p that there exists a function D(n) such that in the space H(n 1, n 2, ···, n r; n, p), ? What is the range of p such that a.e., H p ∈ H (n 1, n 2, ···, n r; n, p) has a unique vertex in V 1 with degree ? Both answers are p = o (log n 1/N), where . The corresponding problems on also are considered, and we obtained the answers are p ≤ (1 + o(1))(log n 1/N) and p = o (log n 1/N), respectively.
相似文献
$${\Delta _{{V_1}}} = {\Delta _{{V_1}}}\left( H \right)$$
$${\delta _{{V_1}}} = {\delta _{{V_1}}}\left( H \right)$$
$${X_{d,{V_1}}} = {X_{d,{V_1}}}\left( H \right),{Y_{d,{V_1}}} = {Y_{d,{V_1}}}\left( H \right)$$
$${Z_{d,{V_1}}} = {Z_{d,{V_1}}}\left( H \right)and{Z_{c,d,{V_1}}} = {Z_{c,d,{V_1}}}\left( H \right)$$
$${X_{d,{V_1}}},{Y_{d,{V_1}}},{Z_{d,{V_1}}}and{Z_{c,d,{V_1}}}$$
$$\mathop {\lim }\limits_{n \to \infty } P\left( {{\Delta _{{V_1}}} = D\left( n \right)} \right) = 1$$
$${\Delta _{{V_1}}}\left( {{H_p}} \right)$$
$$N = \mathop \prod \limits_{i = 2}^r {n_i}$$
$${\delta _{{V_i}}}\left( {{H_p}} \right)$$
20.
On Schwarzian Triangle Functions,Automorphic Forms and a Generalization of Ramanujan’s Triple Differential Equations 下载免费PDF全文
Li Chien Shen 《数学学报(英文版)》2018,34(11):1648-1662
Let G be the group of the fractional linear transformations generated by where m, n is a pair of integers with either n ≥ 2,m ≥ 3 or n ≥ 3,m ≥ 2; τ lies in the upper half plane H.
A fundamental set of functions f0, fi and f∞ automorphic with respect to G will be constructed from the conformal mapping of the fundamental domain of G. We derive an analogue of Ramanujan’s triple differential equations associated with the group G and establish the connection of f0, fi and f∞ with a family of hypergeometric functions. 相似文献
$$T(\tau ) = \tau + \lambda ,S(\tau ) = \frac{{\tau \cos \frac{\pi }{n} + \sin \frac{\pi }{n}}}{{ - \tau \sin \frac{\pi }{n} + \cos \frac{\pi }{n}}};$$
$$\lambda = 2\frac{{\cos \frac{\pi }{m} + \cos \frac{\pi }{n}}}{{\sin \frac{\pi }{n}}};$$