Approximation properties for solutions to non‐Lipschitz stochastic differential equations with Lévy noise

In this paper, we consider the non‐Lipschitz stochastic differential equations and stochastic functional differential equations with delays driven by Lévy noise, and the approximation theorems for the solutions to these two kinds of equations will be proposed respectively. Non‐Lipschitz condition is much weaker condition than the Lipschitz one. The simplified equations will be defined to make its solutions converge to that of the corresponding original equations both in the sense of mean square and probability, which constitute the approximation theorems. Copyright © 2014 John Wiley & Sons, Ltd.     

Standing waves for 4‐superlinear Schrödinger‐Kirchhoff equations

We consider standing waves for 4‐superlinear Schrödinger–Kirchhoff equations in with potential indefinite in sign. The nonlinearity considered in this study satisfies a condition that is much weaker than the classical Ambrosetti–Rabinowitz condition. We obtain a nontrivial solution and, in the case of odd nonlinearity, an unbounded sequence of solutions via the Morse theory and the fountain theorem, respectively. Copyright © 2014 John Wiley & Sons, Ltd.     

An inverse coefficient problem for a quasilinear parabolic equation with periodic boundary and integral overdetermination condition

In this paper, the inverse problem of finding the time‐dependent coefficient of heat capacity together with the solution periodic boundary and integral overdetermination conditions is considered. Under some natural regularity and consistency conditions on the input data, the existence, uniqueness, and continuous dependence upon the data of the solution are shown. Some considerations on the numerical solution for this inverse problem are presented with an example. Copyright © 2014 John Wiley & Sons, Ltd.     

Abundant explicit exact solutions to the generalized nonlinear Schrödinger equation with parabolic law and dual‐power law nonlinearities

This paper is concerned with the generalized nonlinear Schrödinger equation with parabolic law and dual‐power law. Abundant explicit and exact solutions of the generalized nonlinear Schrödinger equation with parabolic law and dual‐power law are derived uniformly by using the first integral method. These exact solutions are include that of extended hyperbolic function solutions, periodic wave solutions of triangle functions type, exponential form solution, and complex hyperbolic trigonometric function solutions and so on. The results obtained confirm that the first integral method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial DEs. Copyright © 2014 John Wiley & Sons, Ltd.     

The Allen–Cahn equation with dynamic boundary conditions and mass constraints

The Allen–Cahn equation, coupled with dynamic boundary conditions, has recently received a good deal of attention. The new issue of this paper is the setting of a rather general mass constraint, which may involve either the solution inside the domain or its trace on the boundary. The system of nonlinear partial differential equations can be formulated as a variational inequality. The presence of the constraint in the evolution process leads to additional terms in the equation and the boundary condition containing a suitable Lagrange multiplier. A well‐posedness result is proved for the related initial value problem. Copyright © 2014 John Wiley & Sons, Ltd.     

解P_0非线性互补问题的光滑Levenberg-Marquardt方法

本文研究了一个P0非线性互补问题.利用信赖域技术获得了求解该问题的光滑Levenberg-Marquardt算法,该算法在一定条件下具有全局性.利用局部误差界还获得了该算法的超线性和二次收敛.数值结果表明该算法是有效的.     

Mild method for the synthesis of 1H-indazoles through oxime-phosphonium ion intermediate

The synthesis of 1H-indazoles from o-aminobenzoximes is achieved via N–N bond formation using triphenylphosphine, I₂, and imidazole. Selective formation of oxime-phosphonium ion intermediate in the presence of the amino group is the driving force for this reaction. The nucleophilicity of the arylamino group and electrophilicity toward the N–O bond of oxime also control the reaction. The reaction proceeds at a faster rate with good to excellent yield under this mild reaction condition and is amenable to scale-up.     

Palladium‐Catalyzed C?S Activation/Aryne Insertion/Coupling Sequence: Synthesis of Functionalized 2‐Quinolinones

The insertion of an aryne into a C S bond can suppress the addition of an S nucleophile to the aryne in the presence of palladium. Catalyzed by Pd(OAc)₂, a wide range of α‐carbamoyl ketene dithioacetals readily react with arynes to selectively afford functionalized 2‐quinolinones in high yields under neutral reaction conditions by a C S activation/aryne insertion/intramolecular coupling sequence. The attractive feature of the new strategy also lies in the versatile transformations of the alkythio‐substituted quinolinone products.