A note on the existence of multiple solutions for a class of systems of second order ODEs

We prove the existence of multiple solutions for some systems of second order ODEs with Dirichlet boundary conditions. Such systems are obtained by coupling scalar ODEs with different growth conditions. The proof relies on a global continuation technique.     

Integrated Fuzzy AHP–TOPSIS for selecting the best plastic recycling method: A case study

Due to the rapid depletion of natural resources and undesired environmental changes in a global scale, it is necessary to conserve the natural resources and protect the environment. Industries which manufacture plastic based products have the necessity to recycle plastics. There are number of methods to recycle plastics. Since the selection of the best recycling method involves complex decision variables, it is considered to be a multiple criteria decision-making (MCDM) problem. This article develops an evaluation model based on the fuzzy Analytic Hierarchy Process (AHP) and the technique for order performance by similarity to ideal solution (TOPSIS) to enable the industry practitioners to perform performance evaluation in a fuzzy environment. The purpose of the study is to determine the best method for recycling plastics among the various plastic recycling processes. By observing the results, it is identified that mechanical recycling process is found to be the best plastic recycling process using the integrated approach.     

Existence theorems for some abstract nonlinear non-autonomous systems with delays

For some abstract classes of nonlinear non-autonomous systems with variable and state-dependent delays existence, non-existence and multiplicity of periodic solutions are discussed. To illustrate the efficiency of the method, we obtain some well-known results for applied systems as corollaries of our existence theorems.     

On integral operators for certain classes of p-valent functions associated with generalized multiplier transformations

In this paper, we study new generalized integral operators for the classes of p-valent functions associated with generalized multiplier transformations.     

Certain subclasses of p-valently analytic functions involving a generalized fractional differintegral operator

By making use of the principle of subordination between analytic functions and the generalized fractional differintegral operator, we introduce and investigate some new subclasses of p-valently analytic functions in the open unit disk. Such results as inclusion relationships, integral-preserving properties, convolution properties, subordination and superordination properties, and sandwich theorems for these classes are derived.     

LK property for σ-ideals

An ideal J of subsets of a Polish space X has (LK) property whenever for every sequence (An) of analytic sets in X, if lim supn∈HAn∉J for each infinite H then _?n∈G∉J for some infinite G. In this note we present a new class of σ-ideals with (LK) property.     

Analytic smoothing effect for global solutions to nonlinear Schrödinger equations

We prove the global existence of analytic solutions to the Cauchy problem for the cubic Schrödinger equation in space dimension n?3 for sufficiently small data with exponential decay at infinity. Minimal regularity assumption regarding scaling invariance is imposed on the Cauchy data.     

Exact and explicit solutions of Euler-Painlevé equations through generalized Cole-Hopf transformations

More general Euler-Painlevé equations are exactly linearized using generalized Cole-Hopf transform and are shown to admit exact solutions in terms of Kummer functions. The asymptotic behaviours of Euler-Painlevé equations are also derived.     

Approximations of solutions to neutral functional differential equations with nonlocal history conditions

This work is concerned with a class of neutral functional differential equations with nonlocal history conditions in a Hilbert space. The approximation of solution to a class of such problems is studied. Moreover, the convergence of Faedo-Galerkin approximation of solution is shown. For illustration, an example is worked out.     

Poisson半群的边界值

在空间Ｌｐ（Ｒｎ），１≤ｐ＜∞中，Ｐｏｉｓｏｎ算子半群ｅ－－△ｚ是右半平面Ｒｅｚ＞０上的解析半群．本文考虑它的边界值，证明了闭稠定算子－ｉ－△对某个α≥０生成了一个指数有界（Ｉ＋－△）－α 半群．