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In this study, the numerous solutions to Falkner–Skan flow of a Maxwell fluid with nanoparticles are investigated, considering the nonlinear radiation and magnetic domain. The flow described above can be expressed in accordance with PDEs that are transformed into ODEs by choosing suitable variables of similarity. The fourth- and fifth-order Runge–Kutta–Fehlberg method can be utilized to solve these reduced ODEs by applying the shooting approach. The graphs were drawn to explain the effects of different parameters on different fluid profiles for both the lower- and upper-branch solutions. This study shows that the velocity outlines improve both solutions by increasing local Deborah numbers slightly. Besides, an increase in radiation reduces the thermal gradient for both solutions, thereby reducing the concentration gradient for both solutions contributing to raised Brownian motion and Lewis numbers.

The recent multiple-solution problem in extracting physics information from a fit to the experimental data in high energy physics is reviewed from a mathematical viewpoint. All these multiple solutions were previously found via a fit process, while in this paper we prove that if the sum of two coherent Breit–Wigner functions is used to fit the measured distribution, there should be two and only two nontrivial solutions, and they are related to each other by analytical formulae. For real experimental measurements in more complicated situations, we also provide a numerical method to derive the other solution from the already obtained one. The excellent consistency between the exact solution obtained this way and the fit process justifies the method. From our results it is clear that the physics interpretation should be very different depending on which solution is selected. So we suggest that all the experimental measurements with potential multiple solutions be re-analyzed to find the other solution because the result is not complete if only one solution is reported.

The cross-sections of $e^{+}{e}^{-}\to h_c{\pi }^{+}{\pi }^{-}$ and ${\chi }_{c0}\omega$ were measured by the BESIII experiment. In both cross-section distributions, there are structures at a mass of about $4220\mathrm{\text{MeV}}∕c^2$. A combined fit is performed to the two cross-section distributions, assuming the structures are due to the same vector resonant state, the $Y(4220)$. The parameters of the $Y(4220)$ are determined using two fit methods. The ratios $\Gamma (Y(4220)\to {\chi }_{c0}\omega )∕\Gamma (Y(4220)\to h_c{\pi }^{+}{\pi }^{-})$ are obtained, which may help in the understanding of the nature of this structure. Although a similar work was done previously, all the multiple solutions in our fits are taken into account and our conclusions are more precise and complete.

In this paper, we address a newly nonlinear Schrödinger equation (NLSE) in $(2+1)$-dimensions influenced by cubic–quintic–septic law nonlinearity and spatial dissipations effects. We properly construct the dark and bright optical soliton solutions for our governing model. Furthermore, periodic, other singular solutions, multiwave, homoclinic breather, M-shaped rational and their interaction with kink waves of various structures will be derived. In addition to this, some 3D, 2D and contour profiles will be added to anticipate the wave dynamics.

We consider the Dirichlet problem associated to the nonhomogenous elliptic equation -Δu = |u|^2*-2u + f with critical exponent on a symmetric domain, and study the impact of symmetries on it. We show that a rich symmetry structure will give rise, in some cases, to many solutions.

Let be the 2-dimensional unit disk and . For suitably small H>0, we consider the Dirichlet problem for H-systems

We consider the problem

In this paper, we study the following concave–convex elliptic problems:

The present paper is concern with the Dirichlet problem for semi-linear corner degenerate elliptic equations with singular potential term. We first give the preliminary of the framework and then discuss the weighted corner type Hardy inequality. By using the variational method, we prove the existence of multiple solutions for the Dirichlet boundary-value problem.

In this paper, we consider the following quasilinear elliptic equation with critical growth and a Hardy term:

where $s\ge 1$, $a$ is a constant, $\mu \ge 0,$$2^{\ast }=\frac{2N}{N-2}$ is the Sobolev critical exponent. And $\mathrm{\Omega }\subset {ℝ}^N$ is an open bounded domain which contains the origin. We will study the existence of infinitely many solutions for (P). To achieve this goal, we first perform various kinds of change of variables to overcome the difficulties caused by the unboundedness of $c_{ij}(t)$ ($|c_{ij}(t)|\sim |t{|}^{2s-2}$ for large $\left|t\right|$) and the lack of a global monotone condition $(G)$ (see below) on $c_{ij}(t)$, then combining the idea of regularization approach and subcritical approximation we prove the existence of infinitely many solutions for (P). Our results show that under some suitable assumptions on $c_{ij}^{\prime }(w)$, without the perturbation of the lower term $a|w{|}^{2(s-1)}w,$ we can still obtain the existence of infinitely many solutions for (P).

Vibration energy is scavenged by a beam system based on magnetostrictive material (MsM). The system consists of interconnected substructural beams (aluminum and magnetostrictive layers) with a neutral stress axis shifted away from the axis of symmetry of the magnetostrictive beam. The coil that generates the electromotive force is wound on the composite beam. The study investigates the effects of a tip mass placed at the end of the beam and the beam thickness influence. Multiple solutions are found for high amplitudes, and the optimal configuration of the operating conditions is proposed. In addition, the sensitivity of the system to the initial conditions is compared for the first three resonance areas, leading to determination of two types of solutions with different levels of power output.

This paper concerns the existence of multiple solutions for a Schrödinger logarithmic equation of the form

In this paper, a model of simultaneous mass and heat transfer within a porous catalyst in a flat particle is considered. A new modification of the shooting reproducing kernel Hilbert space (SRKHS) method is proposed, which is also capable of handling the system of nonlinear boundary value problems by employing Newtons method. The proposed method is a well-performance technique in both predicting and calculating multiple solutions of the nonlinear boundary value problems. Applying the SRKHS method shows that the mentioned model might admit multiple stationary solutions (unique, dual or triple solutions) depending on the values of the parameters of the model. Furthermore, the convergence of the method is proved and some numerical tests reveal the high efficiency of this new version of SRKHS method.

The purpose of the study was to explore prospective elementary teachers’ different approaches to promote their students’ creativity and mathematical creativity. Twenty-one prospective elementary teachers participated in the study. The results indicated that the participants tended to use more approaches to promote their students’ creativity than to promote mathematical creativity. The greatest proportion of the approaches to promote students’ creativity and mathematical creativity was to establish a motivating atmosphere and to encourage multiple solutions to mathematical problems, respectively.

We combine heat flow method with Morse theory, super- and sub-solution method with Schauder's fixed point theorem to show the existence of multiple solutions of the prescribed mean curvature equation under some special circumstances.

We present some multiplicity results concerning Schrödinger type equations which involve nonlinearity with sublinear growth at infinity. The results are based on some recent critical point theorems of B. Ricceri.

The aim of this paper is to present some multiplicity results for elliptic boundary value problems involving oscillating nonlinearities. These results are obtained by using a variational theorem of Ricceri and some developments of this latter.

Using a recent variational principle of B. Ricceri, we present some results of existence of infinitely many solutions for the Dirichlet problem involving the p-Laplacian.

The aim of this paper is to provide suitable conditions under which the following Neumann problem:

We present some of our results concerning the existence of multiple solutions to elliptic differential equations. In particular, we deal with the Dirichlet problem involving the p-Laplacian and the periodic solutions to second order Hamiltonian systems. In all of these results, we follow a variational approach. We look for solutions of the considered problem which are in turn local minima for the underlying energy functional.