Zeitschrift für angewandte Mathematik und Physik最新文献

In this paper, we study a double phase problem with both variable exponents. Such problem has a reaction consisting of a Carathéodory perturbation defined only locally and of a critical term. The presence of the critical term does not permit to use results of the critical point theory for the corresponding energy functional. Consequently, using suitable cut-off functions and truncation techniques we focus on an auxiliary coercive problem on which, differently from our main problem, we can act with variational tools. In this way, we are able to produce a sequence of sign-changing solutions to our main problem converging to 0 in (L^{infty }) and in the Musielak–Orlicz Sobolev space.

The Sharma–Tasso–Olver–Burgers (STOB) equation is a nonlinear partial differential equation that appears in many branches of science, engineering and describes significant phenomena including wave propagation and fluid dynamics. The STOB equation characteristics and solutions for the nonlinear situation are thoroughly examined in this research work. The analytical techniques, namely the extended ((frac{G'}{G^{2}}))-expansion method, stability analysis, and sensitivity analysis, are used to determine the solitons solution of STOB equation. The study begins with an overview of the equation, highlighting its significance in modeling. The nonlinear nature of the equation leads to interesting dynamics and challenges in its analysis and solution. The research paper focuses on understanding the behavior of solutions and identifying the solution with the help of graphical interpretation. Numerous of the identified solutions are depicted in figures to provide a physical comprehension. Because it is critical, we use appropriate values of parameters to highlight the physical aspects of the supplied data using 3D, 2D, and contour charts. The proposed techniques are valuable and contribute to the field of nonlinear sciences. Various nonlinear evolutionary equations are employed to represent models of nonlinear physical phenomena

In this paper, we study the existence of normalized solutions for the nonautonomous Schrödinger–Poisson equations

where (lambda in mathbb {R}), (A in L^infty (mathbb {R}^3)) satisfies some mild conditions. Due to the nonconstant potential A, we use Pohozaev manifold to recover the compactness for a minimizing sequence. For (pin (2,3)), (pin (3,frac{10}{3})) and (pin (frac{10}{3}, 6)), we adopt different analytical techniques to overcome the difficulties due to the presence of three terms in the corresponding energy functional which scale differently.

Mathematical models play a crucial role in controlling and preventing the spread of diseases. Based on the communication characteristics of diseases, it is necessary to take into account some essential epidemiological factors such as the time delay that takes an individual to progress from being latent to become infectious, the infectious age which refers to the duration since the initial infection and the occurrence of reinfection after a period of improvement known as relapse, etc. Moreover, age-structured models serve as a powerful tool that allows us to incorporate age variables into the modeling process to better understand the effect of these factors on the transmission mechanism of diseases. In this paper, motivated by the above fact, we reformulate an SEIR model with relapse and age structure in both latent and infected classes. Then, we investigate the asymptotic behavior of the model by using the stability theory of differential equations. For this purpose, we introduce the basic reproduction number (mathcal {R}_0) of the model and show that this threshold parameter completely governs the stability of each equilibrium of the model. Our approach to show global attractivity is based on the fluctuation lemma and Lyapunov functionals method with some results on the persistence theory. The conclusion is that the system has a disease-free equilibrium which is globally asymptotically stable if (mathcal {R}_0<1), while it has only a unique positive endemic equilibrium which is globally asymptotically stable whenever (mathcal {R}_0>1). Our results imply that early diagnosis of latent infection with decrease in both transmission and relapse rates may lead to control and restrict the spread of disease. The theoretical results are illustrated with numerical simulations, which indicate that the age variable is an essential factor affecting the spread of the epidemic.