In this paper, we study the large time behavior of the Cauchy problem for inhomogeneous Burgers equation. The initial data is assumed to be periodic and the source term has several zero points. We show that under some assumptions on the initial data, the solution approaches to a traveling wave. The main method we used is the theory of generalized characteristics generated by Dafermos C M.
This paper is concerned with the dynamical behaviors of a diffusive predator-prey system with disease and Holling II functional response. We discuss the stability of the nonnegative constant steady states by using the characteristic equation technique and Laypunov functional method. Priori estimates for the system is given by inequality technique and Maximum Principle. Furthermore, we derive some results for the non-existence and existence of non-constant positive solution.
Let X be a compact metric space and f: XX be a continuous map. In this paper, we prove that f is strongly ergodic if f is entropy-minimal.In addition, we show that f has positive topological entropy and fn is ergodically sensitive for any n1 if there exists a proper (quasi) weakly almost periodic point of f , hence f is chaotic in the sense of Li-Yorke and Takens-Ruelle.The presented results improve and generalize some recent results.
We prove that the double inequalities and hold for all a,b>0 with if and only if and .Here, and denote the quadratic, harmonic and Toader means of two positive numbers and , respectively.
A class of inhomogeneous nonlinear elliptic boundary value problem is discussed on compact manifolds with a smooth boundary. The maximum principles are used to obtain the gradient estimates for the solution of the problem. As its application, we obtain the efficiency ratio estimate of the solution.
The aim of this note is to establish the existence of multiple solutions for Sturm-Liouville boundary value problems.Proofs are based on variational methods as developed in the important works of Bonanno. In particular, the existence of three solutions for a Sturm-Liouville problem, even under a perturbation of the nonlinearity, is established.
Let be a function with derivatives of order and The authors in the paper prove that if is homogenous of degree zero and satisfies the mean value zero condition about the variable , then both the generalized higher order Marcinkiewicz integral and itsvariationare bounded on Herz-type Hardy spaces.
In this paper, we prove that the Cauchy problem for the generalized IMBq equations with weak damping,, , admits a unique global generalized solution in~is~real~number) and a unique global classical solution in. We give the sufficient conditionsof the blow up of the solution for the above mentioned Cauchy problem.
The number of limit cycles of a class of symmetric cubic near-Hamiltonian system under symmetric non-smooth perturbations are investigated in this paper. At least 19 limit cycles are found in this class of perturbed non-smooth cubic system by using the method of multi-parameter perturbation theory and qualitative analysis.
Using the Kuratowski measure of noncompactness and progressive estimation method, we study the existence and regularity of mild solutions for damped second order impulsive functional differential equations with infinite delay in Banach spaces. The compactness condition on the impulsive term,some restrictive conditions on a priori estimation and noncompactness measure estimation have not been used, our results are different from the known results.As applications, some examples are provided to illustrate the obtained results.
We establish three series-product identities. Our tools are the Jacobi triple product identity and the method of series rearrangement. Several identities on Dedekind's eta function are obtained.
In this paper, we consider the fuzzy pricing problems for European options with jumps and transaction costs, based on the Merton's jump diffusion model. First, we deduce the pricing formula for European call options with jumps and transactions,and then the fuzzy counterpart of it is given by applying the fuzzy mathematical theory. Also, we provid the disfuzzification method for the obtained European call option pricing formula with the help of fuzzy integration. In the end, some illustrative numerical analysis examples are executed with Sage codes.
The general coupled matrix equations , have numerous applications in control and system theory. In this paper, an algorithm is constructed to solve the general coupled matrix equations where is a bisymmetric matrix with a specified central principal submatrix. The algorithm produces suitable such that is minimized within a finite iteration steps in the absence of roundoff errors. The algorithm requires little storage capacity. Numerical examples are given to show that the algorithm is efficient.
The existence and multiplicity of nontrivial solutions are obtained for the Kirchhoff-type problem {\disp−(a+b∫RN|∇u|2dx)Δu+V(x)u=f(x,u)\qqin\qRN,u∈H1(RN)
In this paper, the limit theorems for function of Markov Chains in random environments are investigated. Moreover, some sufficient conditions for the strong convergence of the weighted sums to hold for function of Markov Chains in random environments are obtained, which extend and improve the related known works for weighted sums of random variables in the literature.
New unique common fixed point results for four mappings satisfying certain Lipschitz type conditions on a non-complete topological vector space-valued cone metric space are obtained, and their corollaries are given. Our main results generalize and improve some well-known recent results in the literatures.
In this paper, we study the generalized operator between different Dirichlet type spaces. For 、 or , we provide sufficient and necessary conditons for to be bounded or compact. Moreover, for other p, we also discuss the sufficient conditions or the necessary conditons forto be bounded or compact.
This paper studies the weakly coupled beam-string systems with local memory damping. First, under the appropriate hypothesis, we proved that the well-posedness of the system by using the theory of linear operator semigroup. And then, we show that the energy of the weakly coupled beam-string system with local memory damping is uniform exponential decay by applying the frequence domain result on Hilbert space.
In this paper, using the estimate of the higher order derivative of the function in mixed norm spaces, the properties of the analytic function andoperator theory, the authorscharacterize the boundedness and compactness of the Volterra-type composition operator from mixed norm spaces to little Zygmund spaces. Some necessary and sufficient conditions of the Volterra-type composition operatorsto be bounded and compact are obtained.
In this paper, the authors study the properties of some complex difference equations, such as the growth, the distribution of zeros and poles of the soultions, and the possible reduced form of the equations. The authors generalize the previous result of Zheng X M and Chen Z X.
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