高阶非线性常微分方程组周期解的存在性

本文考虑非线性常微分方程组周期解的存在性,得到了周期解的Ｎａｇｕｍｏ型先验估计,由此在一般性条件下证明了方程组至少有一个Ｔ－周期解,     

Existence of solutions for a system of equations of nonlinear elastic materials

The question of the existence of solutions for the system of nonlinear partial differential equations governing the arbitrarily heated and prestressed nonhomogeneous shell is considered. We give the sufficient conditions for the existence of at least one solution by way of a fixed point theorem in an appropriate function space.     

A shooting method for a nonlinear beam equation

We study the existence of solutions for a nonlinear fourth-order ODE with nonlinear boundary condition that arises in beam theory. Using a shooting type argument, we prove the existence of at least one solution of the problem.     

Toeplitz matrix method and nonlinear integral equation of Hammerstein type

The existence and uniqueness solution of the nonlinear integral equation of Hammerstein type with discontinuous kernel are discussed. The normality and continuity of the integral operator are proved. Toeplitz matrix method is used, as a numerical method, to obtain a nonlinear system of algebraic equations. Also, many important theorems related to the existence and uniqueness of the produced algebraic system are derived. Finally, numerical examples, when the kernel takes a logarithmic and Carleman forms, are discussed and the estimate error, in each case, is calculated.     

ON THE EXISTENCE OF PERIODIC SOLUTIONS TO A CERTAIN FOURTH-ORDER NONLINEAR DIFFERENTIAL EQUATION

In this paper, we consider a certain fourth-order nonlinear ordinary differential equation. Some sufficient conditions which guarantee the existence of at least one ω-periodic solution to the system are obtain.     

Landesman-Lazer type conditions for a system of p-Laplacian like operators

We study the existence of periodic solutions for a nonlinear second order system of ordinary differential equations of p-Laplacian type. Assuming suitable Nagumo and Landesman-Lazer type conditions we prove the existence of at least one solution applying topological degree methods. We extend a celebrated result by Nirenberg for resonant systems.     

ON THE EXISTENCE THEOREMS OF NONTRIVIAL PERIODIC SOLUTIONS TOA CLASS OF NONLINEAR NON－AUTONOMOUS SYS

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Nonlinear fractional cone systems with the Caputo derivative

Nonlinear fractional cone systems involving the Caputo fractional derivative are considered. We establish sufficient conditions for the existence of at least one cone solution to such systems. Sufficient conditions for the unique existence of the cone solution to a nonlinear fractional cone system are given.     

Existence results for an indefinite unbounded perturbation of a resonant Schrödinger equation

We study existence results for a nonlinear Schrödinger equation at resonance. The nonlinearity is assumed to change sign, be unbounded but sublinear with a power like growth at infinity. Under a suitable coercivity assumption on the primitive of the nonlinear term on the kernel of the Schrödinger operator, we prove the existence of at least one solution.     

Monotone method for a system of nonlinear mixed type implicit impulsive integro-differential equations in Banach spaces

In this paper, by using a monotone iterative technique in the presence of lower and upper solutions, we discuss the existence of solutions for a new system of nonlinear mixed type implicit impulsive integro-differential equations in Banach spaces. Under wide monotonicity conditions and the noncompactness measure conditions, we also obtain the existence of extremal solutions and a unique solution between lower and upper solutions.     

Integral equations and initial value problems for nonlinear differential equations of fractional order

We discuss the solvability of integral equations associated with initial value problems for a nonlinear differential equation of fractional order. The differential operator is the Caputo fractional derivative and the inhomogeneous term depends on the fractional derivative of lower orders. We obtain the existence of at least one solution for integral equations using the Leray–Schauder Nonlinear Alternative for several types of initial value problems. In addition, using the Banach contraction principle, we establish sufficient conditions for unique solutions. Our approach in obtaining integral equations is the “reduction” of the fractional order of the integro-differential equations based on certain semigroup properties of the Caputo operator.     

On a decoupled linear FEM integrator for eddy-current-LLG

We propose a numerical integrator for the coupled system of the eddy-current equation with the nonlinear Landau–Lifshitz–Gilbert equation. The considered effective field contains a general field contribution, and we particularly cover exchange, anisotropy, applied field and magnetic field (stemming from the eddy-current equation). Even though the considered problem is nonlinear, our scheme requires only the solution of two linear systems per time-step. Moreover, our algorithm decouples both equations so that in each time-step, one linear system is solved for the magnetization, and afterwards one linear system is solved for the magnetic field. Unconditional convergence – at least of a subsequence – towards a weak solution is proved, and our analysis even provides existence of such weak solutions. Numerical experiments with micromagnetic benchmark problems underline the performance and the stability of the proposed algorithm.     

Non-asymptotic and potential Landesman-Lazer conditions for a nonlinear beam equation

Existence of solutions for a nonlinear fourth order ordinary differential equation arising in beam theory is considered. We obtain solutions by a degree argument under a non-asymptotic condition on the nonlinear terms of the problem. Moreover, assuming a potential Landesman-Lazer condition, we prove the existence of at least one solution by variational methods.     

On the Existence of Periodic Solutions for a Nonlinear System of Ordinary Differential Equations

Abstract This paper is concerned with the existence of periodic solutions for a nonlinear system of ordinary differential equations. We obtain a Nagumo-type a priori bound for the periodic solutions and then by using this a priori bound we prove the existence of at least one T-periodic solution under some general conditions Research supported by the NNSF of China and the RFDP of China.     

Solvability for a third-order three-point BVP on time scales

We are concerned with the existence of a nontrivial solution to a nonlinear third-order three-point boundary-value problem on general time scales. Using the corresponding Green function, without a non-negative or monotone-type assumption on the nonlinearity, we obtain sufficient conditions for the existence of at least one nontrivial solution, using the Leray–Schauder nonlinear alternative theorem. This paper extends recent results in differential equations to difference equations, quantum equations, and general dynamic equations on time scales.     

Oscillating solutions of a nonlinear fourth order ordinary differential equation

We study the existence of periodic solutions for a nonlinear fourth order ordinary differential equation. Under suitable conditions we prove the existence of at least one solution of the problem applying coincidence degree theory and the method of upper and lower solutions.     

Uniqueness of weak solutions to a non-linear hyperbolic system in electrohydrodynamics

In this note we prove the uniqueness of weak solutions to a nonlinear hyperbolic system in electrohydrodynamics without the effects of a dissociation–recombination process. It is still open in the presence of a special dissociation–recombination process, although the existence of at least one weak solution was proved via the method of renormalized solutions by Feireisl [E. Feireisl, Weak solutions to a non-linear hyperbolic system arising in the theory of dielectric liquids, Math. Methods Appl. Sci. 18 (1995) 1041–1052] in 1995.     

Nagumo and Landesman-Lazer type conditions for nonlinear second order systems

We study the existence of solutions for a nonlinear second order system of ordinary differential equations under various boundary conditions. Assuming suitable Nagumo type conditions we prove the existence of at least one solution applying the method of upper and lower solutions. Moreover, using topological degree methods we prove the existence of solutions under Landesman-Lazer type conditions.     

Multiple Solutions for a Differential Inclusion Problem with Nonhomogeneous Boundary Conditions

In this paper, we use a mountain pass theorem with Cerami type conditions for locally Lipschitz functions to investigate the existence of at least one nontrivial solution for a differential inclusion problem involving the p-Laplacian and with nonlinear and nonsmooth boundary conditions. Moreover, by a symmetric version of the mountain pass theorem, we prove the existence of infinitely many solutions.     

一类无穷多点边值问题正解的存在性

研究一类二阶非线性常微分方程无穷多点边值问题正解的存在性,利用不动点指数理论得到了方程至少存在一个正解的若干充分条件.