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This paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.

This paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.

This paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.

This article is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.

The reduced problem of the Navier–Stokes and the continuity equations, in two-dimensional Cartesian coordinates with Eulerian description, for incompressible non-Newtonian fluids, is considered. The Ladyzhenskaya model, with a non-linear velocity dependent stress tensor is adopted, and leads to the governing equation of interest. The reduction is based on a self-similar transformation as demonstrated in existing literature, for two spatial variables and one time variable, resulting in an ODE defined on a semi-infinite domain. In our search for classical solutions, existence and uniqueness will be determined depending on the signs of two parameters with physical interpretation in the equation. Illustrations are included to highlight some of the main results.

Organizational equilibrium theory is a theory of an inducements‐contributions balance within organizations; i.e. it ultimately aims to find conditions for organizational survival. Based on the Simon‐Smithburg‐Thompson postulates for the organizational equilibrium theory, an organizational equilibrium model under uncertainty is constructed. Using a multiple objective satisficing problem formulation, the survival conditions (i.e. existence conditions of viable solutions) are studied. The existence of uniformly better solutions than a given viable solution is also shown. Then, a unique solution (i.e. viable Pareto solution) is defined, and a problem whose solutions are viable Pareto solutions is specified. Finally, several organizational factors involved with the organizational equilibrium concept are discussed.

This paper aims to theoretically and numerically investigate the steady two-dimensional (2D) Hiemenz flow with heat transfer of Reiner-Rivlin fluid over a linearly stretching/shrinking sheet.

The Navier–Stokes equations are transformed into self-similar equations using appropriate similarity transformations and then solved numerically by using shooting technique. A simple but effective mathematical analysis has been used to prove the existence of a solution for stretching case (λ> 0). Moreover, an attempt has been laid to carry the asymptotic solution behavior for large stretching. The obtained asymptotic solutions are compared with direct numerical solutions, and the comparison is quite remarkable.

It is observed that the self-similar equations exhibit dual solutions within the range [λ_c, −1] of shrinking parameter λ, where λ_c is the turning point from where the dual solutions bifurcate. Unique solution is found for all stretching case (λ > 0). It is noticed that the effects of cross-viscous parameter L and shrinking parameter λ on velocity and thermal fields show opposite character in the dual solution branches. Thus, a linear temporal stability analysis is performed to determine the basic feasible solution. The stability analysis is based on the sign of the smallest eigenvalue, where positive or negative sign leading to a stable or unstable solution. The stability analysis reveals that the first solution is stable that describes the main flow. Increase in cross-viscous parameter L resulting in a significant increment in skin friction coefficient, local Nusselt number and dual solutions domain.

This work’s originality is to examine the combined effects of cross-viscous parameter and stretching/shrinking parameter on skin friction coefficient, local Nusselt number, velocity and temperature profiles of Hiemenz flow over a stretching/shrinking sheet. Although many studies on viscous fluid and nanofluid have been investigated in this field, there are still limited discoveries on non-Newtonian fluids. The obtained results can be used as a benchmark for future studies of higher-grade non-Newtonian flows with several physical aspects. All the generated results are claimed to be novel and have not been published elsewhere.

The aim of this work consists of studying numerically the coupling between natural convection and radiation in a tall rectangular cavity by examining the effect of the emissivity of the walls, ε, the Rayleigh number, Ra, and the inclination of the cavity, θ, on the flow characteristics and the existence ranges of the multiple solutions obtained.

The Navier‐Stokes equations were discretized by using a finite difference technique. The vorticity and energy equations were solved by the alternating direction implicit method. Values of the stream function were obtained by using the point successive over‐relaxation method. The calculation of the radiative heat exchange between the walls of the cavity is based on the radiosity method.

For an inclined cavity (θ=45°), up to four different solutions are obtained and their range of existence is found to be strongly dependent on the Rayleigh number and the emissivity of the cavity walls. In the case of a vertical cavity (θ=90°), the weak reduction of the convection effect due to radiation is largely compensated for by the contribution of the radiation which enhances the overall heat transfer through the cold surface of the cavity and favours the appearance of secondary cells.

The existence of multiple steady‐state solutions in an inclined cavity (θ=45°) and the number of the obtained solutions are affected by the presence of radiation. In face, the increase of the emissivity reduces the number of solutions for weak values of the Rayleigh number. Also, the increase of this parameter favours the multiplicity of solutions for all the considered values of the emissivity. For a vertical cavity (θ=90°), the effect of radiation generates an oscillatory convection for large values of the Rayleigh number.

The purpose of this paper is to show the existence results for adapted solutions of infinite horizon doubly reflected backward stochastic differential equations with jumps. These results are applied to get the existence of an optimal impulse control strategy for an infinite horizon impulse control problem.

The main methods used to achieve the objectives of this paper are the properties of the Snell envelope which reduce the problem of impulse control to the existence of a pair of right continuous left limited processes. Some numerical results are provided to show the main results.

In this paper, the authors found the existence of a couple of processes via the notion of doubly reflected backward stochastic differential equation to prove the existence of an optimal strategy which maximizes the expected profit of a firm in an infinite horizon problem with jumps.

In this paper, the authors found new tools in stochastic analysis. They extend to the infinite horizon case the results of doubly reflected backward stochastic differential equations with jumps. Then the authors prove the existence of processes using Envelope Snell to find an optimal strategy of our control problem.

As pointed out by Simon, the “satisficing” decision criterion is one of the most fundamental principles which describe human behaviors. Its mathematical representation i.e., a “satisficing” (decision) problem, is specified by Mesarovic as follows. “Find a decision alternative whose performance is equal to or greater than a given aspiration level for each uncertainty.” Of the results already published about such “satisficing” problems, Mesarovic and Takahara's existence theorem of ‘satisficing’ solutions is most important. However, it requires relatively tight assumptions. Hence, the objective of this paper is to generalize it, in order to enhance its applicability. This is fulfilled by the application of the Teichmüller and Tukey Lemma.

This paper aims to apply an iterative numerical method to find the numerical solution of the nonlinear non-self-adjoint singular boundary value problems that arises in the theory of epitaxial growth.

The proposed problem has multiple solutions and it is singular too; so not every technique can capture all the solutions. This study proposes to use variational iterative numerical method and compute both the solutions. The computed solutions are very close to the exact result.

It turns out that the existence or nonexistence of numerical solutions fully depends on the value of a parameter. The authors show that numerical solutions exist for small positive values of this parameter. For large positive values of the parameter, they find nonexistence of solutions. They also observe existence of solutions for negative values of the parameter and determine the range of parameter values which separates existence and nonexistence of solutions. This parameter has a clear physical meaning, as it describes the rate at which new material is deposited onto the system. This fact allows interpreting the physical significance of the results.

The authors could capture both the solutions and got accurate estimation of the parameter. This method will be a great tool to handle such types of nonlinear non-self-adjoint equations that have multiple solutions in engineering and mathematical sciences. The results in this paper will have an impact on the understanding of theoretical models of epitaxial growth in near future.

In this paper, the authors give a new version of the sub-super solution method and prove the existence of positive solution for a (p, q)-Laplacian system under weak assumptions than usually made in such systems. In particular, nonlinearities need not be monotone or positive.

The authors prove that the sub-super solution method can be proved by the Shcauder fixed-point theorem and use the method to prove the existence of a positive solution in elliptic systems, which appear in some problems of population dynamics.

The results complement and generalize some results already published for similar problems.

The result is completely new and does not appear elsewhere and will be a reference for this line of research.

The purpose of this paper is to find the solution for special cases of regular-long wave equations with fractional order using q-homotopy analysis transform method (q-HATM).

The proposed technique (q-HATM) is the graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme and fractional derivative defined with Atangana-Baleanu (AB) operator.

The fixed point hypothesis considered to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional-order model. To illustrate and validate the efficiency of the future technique, the authors analysed the projected nonlinear equations in terms of fractional order. Moreover, the physical behaviour of the obtained solution has been captured in terms of plots for diverse fractional order.

To illustrate and validate the efficiency of the future technique, we analysed the projected nonlinear equations in terms of fractional order. Moreover, the physical behaviour of the obtained solution has been captured in terms of plots for diverse fractional order. The obtained results elucidate that, the proposed algorithm is easy to implement, highly methodical, as well as accurate and very effective to analyse the behaviour of nonlinear differential equations of fractional order arisen in the connected areas of science and engineering.