Existence of Three Solutions for a Degenerate Kirchhoff–Type Transmission Problem

In this article, we establish the existence of three weak solutions for a nonlinear transmission problem involving degenerate nonlocal coefficients of p(x)–Kirchhoff–type. Our approach is of variational nature; the weak formulation takes place in suitable variable exponent Sobolev spaces.     

Global Existence of Positive Solutions for Volterra Integral Equations

ＧｌｏｂａｌＥｘｉｓｔｅｎｃｅｏｆＰｏｓｉｔｉｖｅＳｏｌｕｔｉｏｎｓｆｏｒＶｏｌｔｅｒｒａＩｎｔｅｇｒａｌＥｑｕａｔｉｏｎｓＷａｎｇＳｈｕ（王术）；ＷａｎＣｈｕｎｌｉｎ（万春林）；ＺｈａｎｇＫｕｎ（张锟）（ＨｅｍａｎＵｎｉｖｅｒｓｉｔｙ，Ｋａｉｆｅｎ...     

The Dirichlet Problem for a Class of Nonlinear Elliptic Equations

In this paper, we study the Dirichlet problem for the nonlinear an isotropic elliptic equation where is a bounded domain, m_i(i=1, 2, …, n) are positive integers, and a_(ij)(x)(i,j=1,2,…,n) are measurable functions on Ω. The Dirichlet problem for semilinear elliptic equation, (1) with m_i=1 (i=1,2,…, n), has been studied by several people, see e.g [1] and the bibliography in [1]. The general nonlinear problem(1) seems to be studied very little.     

Optimality Conditions for Smooth Monge Solutions of the Monge–Kantorovich problem

The Monge–Kantorovich problem (MKP) with given marginals defined on closed domains and a smooth cost function is considered. Conditions are obtained (both necessary ones and sufficient ones) for the optimality of a Monge solution generated by a smooth measure-preserving map . The proofs are based on an optimality criterion for a general MKP in terms of nonemptiness of the sets for special functions on X × X generated by c and f. Also, earlier results by the author are used when considering the above-mentioned nonemptiness conditions for the case of smooth .     

Infinitely Multiple Eigenvalues of The Dirichlet Problem for Quasilinear Elliptic Equations

In this paper, We consider the following Dirichlet problem for quasilinearelliptic equation ( /x_i)F_i(x,Du)=-λu-p(x,u) x∈Ω(1) u| Ω=0     

Weighted Calderón-Zygmund Estimates for Weak Solutions of Quasi-Linear Degenerate Elliptic Equations

Potential Analysis - This paper studies regularity estimates in Sobolev spaces for weak solutions of a class of degenerate and singular quasi-linear elliptic problems of the form...     

The Dirichlet Problem for a Class of Quasilinear Elliptic Equations of Second Order

In this paper,we consider the Dirichlet problem for the quasilinear ellipticequation sum from i=1 to n D_i[a_i(x,Du)]+f(x,u)=0 in Ω, u=0 on Ω,where Ω R~n is a bounded domain. Let p_i>1(i=1,2,…,n),p~*=max p_i and let 1≤i≤n     

Hölder Continuity of Solutions of Nondivergent Degenerate Second-Order Elliptic Equations

One considers a degenerate nondivergent second-order linear elliptic equation. In the model case, the matrix of its higher-order coefficients is diagonal and its elements are powers of the moduli of the independent variables. A sufficient condition on the power exponents is obtained which ensures interior a priori Hölder estimates of the solutions.     

Concentrations Problem for Solutions to Compressible Navier–Stokes Equations

Doklady Mathematics - A three-dimensional initial-boundary value problem for the isentropic equations of the dynamics of a viscous gas is considered. The concentration phenomenon is that, for...     

On the Dirichlet Problem for a Class of Singular Complex Monge–Ampère Equations

We study the Dirichlet problem of the n-dimensional complex Monge–Ampère equation det(uij) = F/|z|~(2α), where 0 α n. This equation comes from La Nave–Tian's continuity approach to the Analytic Minimal Model Program.     

Global Existence and Lifespan of Solutions to the Cauchy Problems for the Nonlinear Schrodinger Equations

Ｇｌｏｂａｌ　Ｅｘｉｓｔｅｎｃｅ　ａｎｄ　Ｌｉｆｅｓｐａｎ　ｏｆ　Ｓｏｌｕｔｉｏｎｓ　ｔｏ　ｔｈｅ　Ｃａｕｃｈｙ　Ｐｒｏｂｌｅｍｓ　ｆｏｒ　ｔｈｅ　Ｎｏｎｌｉｎｅａｒ　Ｓｃｈｒｏｄｉｎｇｅｒ　ＥｑｕａｔｉｏｎｓＧｌｏｂａｌＥｘｉｓｔｅｎｃｅａｎｄＬｉ...     

Local and Global Existence of Solutions to Initial Value Problems of Nonlinear Kaup-Kupershmidt Equations

This paper is devoted to studying the initial value problems of the nonlinear Kaup Kupershmidt equations δu/δt ＋ α1 uδ^2u/δx^2 ＋ βδ^3u/δx^3 ＋ γδ^5u/δx^5 = 0, （x,t）∈ E R^2, and δu/δt ＋ α2 δu/δx δ^2u/δx^2 ＋ βδ^3u/δx^3 ＋ γδ^5u/δx^5 = 0, （x, t） ∈R^2. Several important Strichartz type estimates for the fundamental solution of the corresponding linear problem are established. Then we apply such estimates to prove the local and global existence of solutions for the initial value problems of the nonlinear Kaup- Kupershmidt equations. The results show that a local solution exists if the initial function u0（x） ∈ H^s（R）, and s ≥ 5/4 for the first equation and s≥301/108 for the second equation.     

Existence Theorem of Global Solutions for Monge-Ampere Equation

ＥｘｉｓｔｅｎｃｅＴｈｅｏｒｅｍｏｆＧｌｏｂａｌＳｏｌｕｔｉｏｎｓｆｏｒＭｏｎｇｅ－ＡｍｐｅｒｅＥｑｕａｔｉｏｎｈｏＬｉｊｉａｎｇ（鹿立江）（ＴｉａｎｊｉｎＵｎｉｖｅｒｓｉｔｙｏｆＦｉｎａｎｃｅａｎｄＥｃｏｎｏｍｉｃｓ，Ｔｉａｎｊｉｎ，３００２２２）...     

Abstract Cyclical Monotonicity and Monge Solutions for the General Monge–Kantorovich Problem

Abstract cyclical monotonicity is studied for a multivalued operator F : X L, where L R ^X . A criterion for F to be L-cyclically monotone is obtained and connections with the notions of L-convex function and of its L-subdifferentials are established. Applications are given to the general Monge–Kantorovich problem with fixed marginals. In particular, we show that in some cases the optimal measure is unique and generated by a unique (up to the a.e. equivalence) optimal solution (measure preserving map) for the corresponding Monge problem.     

Existence and nonexistence to exterior Dirichlet problem for Monge–Ampère equation

We consider the exterior Dirichlet problem for Monge–Ampère equation with prescribed asymptotic behavior. Based on earlier work by Caffarelli and the first named author, we complete the characterization of the existence and nonexistence of solutions in terms of their asymptotic behaviors.     

Boundary H¨older Estimates for a Class of Degenerate Elliptic Equations in Piecewise Smooth Domains*

In this paper, the authors will apply De Giorgi-Nash-Moser iteration to establish boundary H¨older estimates for a class of degenerate elliptic equations in piecewise C2smooth domains.     

Stability of Solutions for a Class of Quasilinear Degenerate Parabolic Equations

ＳｔａｂｉｌｉｔｙｏｆＳｏｌｕｔｉｏｎｓｆｏｒａＣｌａｓｓｏｆＱｕａｓｉｌｉｎｅａｒＤｅｇｅｎｅｒａｔｅＰａｒａｂｏｌｉｃＥｑｕａｔｉｏｎｓ￥ＺｈａｏＪｕｎｎｉｎｇ（赵俊宁）（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔ...     

Existence of Solutions to a Singular Initial Value Problem

Under the sign assumptions we investigate the global existence of solutions of the initial value problem x＇ =f（t, x, x＇）, x（0） = A, where the scalar function f（t, x,p） may be singular at x = A.     

The Global Existence of Solutions for a Cross-Diffusion System

ＴｈｅＧｌｏｂａｌＥｘｉｓｔｅｎｃｅｏｆＳｏｌｕｔｉｏｎｓｆｏｒａＣｒｏｓｓ－ＤｉｆｆｕｓｉｏｎＳｙｓｔｅｍ￥（娄元）（倪维明）（吴雅萍）ＹｕａｎＬｏｕ；Ｗｅｉ－ＭｉｎｇＮｉ（ＳｃｈｏｏｌｏｆＭａｔｈｅｍａｔｉｃｓ，ＵｎｉｖｅｒｓｉｔｙｏｆＭｉｎｎｅ...