一类半线性抛物边值问题的最大值原理

文中构造了一类具有Dirichlet或Neumann边界条件的半线性抛物方程u_t=Δu+f(x,u,q,t) (q=|u|^2)的解的一个辅助函数，对其使用Hopf最大值原理和黎曼几何理论，从而获得了该函数的最大值原理，据此原理获得了梯度q和解u的估计.     

Regularity for solutions to anisotropic obstacle problems

For Ω a bounded subset of R n,n 2,ψ any function in Ω with values in R∪{±∞}andθ∈W1,(q i)(Ω),let K(q i)ψ,θ(Ω)={v∈W1,(q i)(Ω):vψ,a.e.and v-θ∈W1,(q i)0(Ω}.This paper deals with solutions to K(q i)ψ,θ-obstacle problems for the A-harmonic equation-divA(x,u(x),u(x))=-divf(x)as well as the integral functional I(u;Ω)=Ωf(x,u(x),u(x))dx.Local regularity and local boundedness results are obtained under some coercive and controllable growth conditions on the operator A and some growth conditions on the integrand f.     

二阶微分方程多点边值问题的三重正解

We consider the second-order differential equation u(t) + q(t)f(t,u(t),u (t)) = 0,0 t 1,subject to three-point boundry condition u(0) = 0,u(1) = a 0 u(ξ 0 ),or to m-point boundary conditionu (0) = m2 i=1 b i u (ξ i ),u(1) = m2 i=1 a i u(ξ i ).We show the existence of at least three positive solutions of the above multi-point boundary-value problem by applying a new fixed-point theorem introduced by Avery and Peterson.     

p-Laplacian算子方程在射线上多点边值问题三个正解的存在性

利用Avery-Peterson不动点定理,在射线上讨论了如下p-Laplacian算子方程多点边值问题,{(φp(u′))′(t)+q(t)f(t,u(t),u′(t))=0,0相似文献   

Positive solutions to m-point boundary value problem of fractional differential equation

In this paper, we study the multiplicity of positive solutions to the following m-point boundary value problem of nonlinear fractional differential equations: Dqu(t) + f(t, u(t)) = 0, 0 < t < 1, u(0) = 0, u(1) =sum (μiDpu(t)|t = ξi ) from i =1 to ∞ m-2, where q ∈R , 1 相似文献   

星图上非线性分数阶微分方程边值问题解的存在唯一性

该文运用Banach压缩映射原理和Schaefer不动点定理研究星图上的非线性分数阶微分方程边值问题{CDα0,xui(x)=fi(x,ui(x),CDβ0,xui(x)),0 ＜ x ＜li,i =1,2,…,k,u′i(0) =ui(1) =0,i =1,2,…,k,u″i (li)=u″j(lj),i,j =1,...     

Coefficient multipliers of mixed norm space in the ball Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

In the paper, we characterize the coefficient multiplier spaces of mixed norm spaces (Hp,q((?)1),Hu,v((?)2)) for the values of p, q, u, v in three cases: (i)0相似文献   

临界增长拟线性椭圆方程的正则性

近年来,非线性临界增长椭圆方程得到了广泛的研究.对于半线性方程,许多正则性结果已经得到.本文我们考虑拟线性方程-sum from i=sum from i=1 to N (?)/((?)_x_i)(α_i(x,u,▽u))=α(x,u,▽u),x∈(?)(?)R~N (1)的 W~((?),p)(?)弱解的正则性.假定α_i(x,z,q),α(x,z,q)是(?)×R×R~N 上的 Carathéodory 函数,且满足如     

MULTIPLE POSITIVE SOLUTIONS FOR QUASILINEAR ELLIPTIC PROBLEMS INVOLVING CONCAVE-CONVEX NONLINEARITIES AND MULTIPLE HARDY-TYPE TERMS

In this paper, we deal with the existence and multiplicity of positive solutions for the quasilinear elliptic problem??pu?kX i=1 μi |u|p?2|x?ai|p u=|u|p*?2 u+λ|u|q?2 u, x∈?, where??RN (N ≥3) is a smoot...     

p(x)-Laplace方程的强极大值原理

本文给出了如下形式的p(x)-Laplace方程-div(| u|p(x)-2 u)+d(x)|u|q(x)-2u=o,x∈Ω的一个强极大值原理,其中p(x),q(x),d(x)满足一定的条件.     

On the coincidence of maximal stable bridges in two approach game problems for stationary control systems

In the present paper we deal with fully nonlinear two-dimensional smooth control systems with scalar input $ \dot q = f(q,u),q \in M,u \in U $ \dot q = f(q,u),q \in M,u \in U , where M and U are differentiable smooth manifolds of respective dimensions two and one. For such systems, we provide two microlocal normal forms, i.e., local in the state-input space, using the fundamental necessary condition of optimality for optimal control problems: the Pontryagin maximum principle. One of these normal forms will be constructed around a regular extremal, and the other one will be constructed around an abnormal extremal. These normal forms, which in both cases are parametrized only by one scalar function of three variables, lead to a nice expression for the control curvature of the system. This expression shows that the control curvature, a priori defined for normal extremals, can be smoothly extended to abnormals.     

On the two-gap elliptic potentials

The-parametrized family of two-gap elliptic potentials is constructed so that (i) 0<<1, (ii) for rational values of such potentials are elliptic (i.e., double-periodic), (iii) within the limit0 this family degenerates to the soliton potential, (iv) within the limit1 this family degenerates to the one-gap Lamé potential.Dedicated to the memory of J.-L. Verdier     

Sufficient conditions that the minimum and maximum of partial differential operators should coincide and that their spectra should be discrete

An expression of the form $$l(u) = ( - 1)^m \sum\nolimits_{j = 1}^m {D_j^{2m} } u + [q(x)] + ir(x)]u$$ is considered. Sufficient conditions are found such that the minimum operator, formally conjugate tol(u), generated by the expression and the maximum operator generated by the expressionl(u) in ?₂ (E_n) should coincide. It is proved that if q(x)→∞ or q(x)+ r(x)→∞, ¦x¦→∞, then the operator generated byl(u) in ?₂ (E_n) has a discrete spectrum.     

Existence Results for Superlinear Elliptic Equations with Nonlinear Boundary Value Conditions

In this paper, we study the existence of solutions for the following superlinear elliptic equation with nonlinear boundary value condition $$\left\{ {\begin{array}{*{20}{c}} { - \Delta u + u = {{\left| u \right|}^{r - 2}}u}&{in\;\Omega ,\;\;} \\ {\frac{{\partial u}}{{\partial v}} = {{\left| u \right|}^{q - 2}}u}&{on\;\partial \Omega ,} \end{array}} \right.$$ where Ω ⊂ ℝN, N ≥ 3 is a bounded domain with smooth boundary. We will prove the existence results for the above equation under four different cases: (i) Both q and r are subcritical; (ii) r is critical and q is subcritical; (iii) r is subcritical and q is critical; (iv) Both q and r are critical.     

关于Fujita型反应扩散方程组的Cauchy问题

本文研究Ｆｕｊｉｔａ型反应扩散方程组ｕｔ－Δｕ＝α１｜ｕ｜ｑ１－１ｕ＋β１｜ｖ｜ｐ１－１ｖ，（ｘ∈ＲＮ，ｔ＞０），ｖｔ－Δｖ＝α２｜ｕ｜ｑ２－１ｕ＋β２｜ｖ｜ｐ２－１ｖ，ｕ（ｘ，０）＝ｕ０（ｘ）０，ｖ（ｘ，０）＝ｖ０（ｘ）０，（ｘ∈ＲＮ）Ｌｐ解的整体存在性和有限时间Ｂｌｏｗ ｕｐ问题．这里ｑｉ＞１，ｐｉ＞１（ｉ＝１，２），α１０，α２＞０，β１＞０，β２０，１ｐ＋∞．     

不连续三阶两点边值问题的可解性

证明了非线性三阶两点边值问题u′″（t）-q（u″（t））f（t，u（t）），u（O）=a，u（1）=b，u″（0）=c解的一个存在定理．在这个问题中，f（t，u）是一个Carathéodory函数而边界条件是非齐次的．我们的结论表明该问题能够有一个解，只要在R。的某个有界集合上q（υ）的“本性高度”与f（t，u）的“最大高度”积分的乘积是适当的．     

有界域上具有离散全纯核的Koppelman公式与方程

D是C^n空间中具有逐块C(1)边界的有界域，该文建立了D上一个具有离散局部全纯核的(0，q)形式的Koppelman积分公式及其相应的方程解的积分表示和它的内闭一致估计式。