Existence and stability of the doubly nonlinear anisotropic parabolic equation

In this paper, we are concerned with a doubly nonlinear anisotropic parabolic equation, in which the diffusion coefficient and the variable exponent depend on the time variable t. Under certain conditions, the existence of weak solution is proved by applying the parabolically regularized method. Based on a partial boundary value condition, the stability of weak solution is also investigated

Lions-type theorem of the p-Laplacian and applications

In this article, our aim is to establish a generalized version of Lions-type theorem for the p-Laplacian. As an application of this theorem, we consider the existence of ground state solution for the quasilinear elliptic equation with the critical growth

Game between the third party payment service provider and bank in mobile payment market

With the innovation and integration of the Internet and the financial industry, the third-party payment market has developed greatly and has great potential. This paper discusses the duopoly game between third-party payment service providers and banks, which are the main participants in the mobile payment market. By constructing Nash game model, the conditions of equilibrium point, stability and bifurcation are analyzed. The effects of adjusting parameters and cooperation coefficient on business volume and profit are discussed. The conclusions are as follows: excessive investment will lead to unpredictable fluctuations in the market and fall into chaos; By strengthening cooperation, all participants in the mobile payment industry chain can improve business volume and profits while curbing chaos in the mobile payment market

Some results on the 1D linear wave equation with van der Pol type nonlinear boundary conditionsand the Korteweg-de Vries-Burgers equation

Many physical phenomena can be described by nonlinear models. The last few decades have seen an enormous growth of the applicability of nonlinear models and of the development of related nonlinear concepts. This has been driven by modern computer power as well as by the discovery of new mathematical techniques, which include two contrasting themes: (i) the theory of dynamical systems, most popularly associated with the study of chaos, and (ii) the theory of integrable systems associated, among other things, with the study of solitons. In this dissertation, we study two nonlinear models. One is the 1-dimensional vibrating string satisfying wtt − wxx = 0 with van der Pol boundary conditions. We formulate the problem into an equivalent first order hyperbolic system, and use the method of characteristics to derive a nonlinear reflection relation caused by the nonlinear boundary conditions. Thus, the problem is reduced to the discrete iteration problem of the type un+1 = F (un). Periodic solutions are investigated, an invariant interval for the Abel equation is studied, and numerical simulations and visualizations with different coefficients are illustrated. The other model is the Korteweg-de Vries-Burgers (KdVB) equation. In this dissertation, we proposed two new approaches: One is what we currently call First Integral Method, which is based on the ring theory of commutative algebra. Applying the Hilbert-Nullstellensatz, we reduce the KdVB equation to a first-order integrable ordinary differential equation. The other approach is called the Coordinate Transformation Method, which involves a series of variable transformations. Some new results on the traveling wave solution are established by using these two methods, which not only are more general than the existing ones in the previous literature, but also indicate that some corresponding solutions presented in the literature contain errors. We clarify the errors and instead give a refined result

Traveling wave phenomena in a nonlocal dispersal predator-prey system with the Beddington-DeAngelis functional response and harvesting

This paper is devoted to studying the existence and nonexistence of traveling wave solution for a nonlocal dispersal delayed predator-prey system with the Beddington-DeAngelis functional response and harvesting. By constructing the suitable upper-lower solutions and applying Schauder\u27s fixed point theorem, we show that there exists a positive constant c∗ such that the system possesses a traveling wave solution for any given c\u3ec∗. Moreover, the asymptotic behavior of traveling wave solution at infinity is obtained by the contracting rectangles method. The existence of traveling wave solution for c=c∗ is established by means of Corduneanu\u27s theorem. The nonexistence of traveling wave solution in the case of

Multiple positive solutions to the fractional Kirchhoff problem with critical indefinite nonlinearities

This article concerns the existence and multiplicity of positive solutions to the fractional Kirchhoff equation with critical indefinite nonlinearities by applying the Nehari manifold approach and fibering maps

A nonautonomous predator–prey system with stage structure and double time delays

AbstractIn the present paper we study a nonautonomous predator–prey model with stage structure and double time delays due to maturation time for both prey and predator. We assume that the immature and mature individuals of each species are divided by a fixed age, and the mature predator only attacks the immature prey. Based on some comparison arguments we discuss the permanence of the species. By virtue of the continuation theorem of coincidence degree theory, we prove the existence of positive periodic solution. By means of constructing an appropriate Lyapunov functional, we obtain sufficient conditions for the uniqueness and the global stability of positive periodic solution. Two examples are given to illustrate the feasibility of our main results

EXISTENCE AND BEHAVIOR OF POSITIVE SOLUTIONS TO ELLIPTIC SYSTEM WITH HARDY POTENTIAL

In this article, we study a class of elliptic systems with Hardy potentials. We analyze the possible behavior of radial solutions to the system when p; t \u3e 1, q; s \u3e 0 and λ; μ \u3e (N - 2)2=4, and obtain the existence of positive solutions to the system with the Dirichlet boundary condition under certain conditions. When λ; μ \u3e 0, p; t \u3e 1 and q; s \u3e 0, we show that any radial positive solution is decreasing in r