Existence and uniqueness of solutions to nonlinear evolution equations with locally monotone operators

In this paper we establish the existence and uniqueness of solutions for nonlinear evolution equations on a Banach space with locally monotone operators, which is a generalization of the classical result for monotone operators. In particular, we show that local monotonicity implies pseudo-monotonicity. The main results are applied to PDE of various types such as porous medium equations, reaction–diffusion equations, the generalized Burgers equation, the Navier–Stokes equation, the 3D Leray-α model and the p-Laplace equation with non-monotone perturbations.     

Existence and uniqueness for nonlinear anisotropic elliptic equations

We study the existence and uniqueness for weak solutions to some classes of anisotropic elliptic Dirichlet problems with data belonging to the natural dual space.     

Existence, uniqueness and stability of Cm solutions of iterative functional equations

In this paper we discuss a relatively general kind of iterative functional equation G(x,f(x),..., fn(x))=0 (for all x∈J), where J is a connected closed subset of the real number axis R, G∈Cm(Jn+1, R), and n≥2. Using the method of approximating fixed points by small shift of maps, choosing suitable metrics on functional spaces and finding a relation between uniqueness and stability of fixed points of maps of general spaces, we prove the existence, uniqueness and stability of Cm solutions of the above equation for any integer m≥0 under relatively weak conditions, and generalize related results in reference in different aspects.     

Existence, uniqueness and stability ofC m solutions of iterative functional equations

In this paper we discuss a relatively general kind of iterative functional equation G(x,f(x), ...,f ⁿ (x)) = 0 (for allx ∈J), whereJ is a connected closed subset of the real number axis ?,G∈C ^m (J ⁿ⁺¹, ?) andn ≥ 2. Using the method of approximating fixed points by small shift of maps, choosing suitable metrics on functional spaces and finding a relation between uniqueness and stability of fixed points of maps of general spaces, we prove the existence, uniqueness and stability ofCm solutions of the above equation for any integer m ≥ 0 under relatively weak conditions, and generalize related results in reference in different aspects.     

Existence,uniqueness and stability of solutions for a class of nonlinear integral equations under generalized Lipschitz condition

In this paper, we prove the existence, uniqueness and the stability of solutions for some nonlinear functional-integral equations by using generalized Lipschitz condition. We prove a fixed point theorem to obtain the mentioned aims in Banach space X:= C([a, b],R). As application we study some Volterra integral equations with linear, nonlinear and singular kernel.     

Existence and uniqueness results for periodic solution of nonlinear differential equations

The existence and uniqueness of solutions for a class of 2nd-order differential equations with periodic conditions are discussed.     

非线性一阶常微分方程解的存在惟一性

讨论了一类非线性一阶常微分方程边值问题解的存在惟一性.得到了当参数在一定的范围取值时解存在惟一的充分条件,并包含了一些已知结果.主要结果基于Leray-Schauder非线性抉择理论和Banach不动点定理.     

Existence and uniqueness of solutions for the nonlinear impulsive fractional differential equations

In this paper, we investigate existence and uniqueness of solutions for nonlinear impulsive fractional differential equations. By utilizing the well-known fixed point theorems, we obtain some sufficient conditions for the uniqueness and existence of the solutions. At the end of the paper, an example is given to illustrate our main results.     

Linearized stability for nonlinear evolution equations

We present a general principle of linearized stability at an equilibrium point for the Cauchy problem , for an -accretive, possibly multivalued, operator in a Banach space , that has a linear 'resolvent-derivative' . The result is applied to derive linearized stability results for the case of under 'minimal' differentiability assumptions on the operators and at the equilibrium point, as well as for partial differential delay equations. RID="h1" ID="h1"To the memory of Philippe Bénilan     

Existence and uniqueness of fuzzy solution for the nonlinear fuzzy integrodifferential equations

In this paper, existence and uniqueness of fuzzy solution for the nonlinear fuzzy integrodifferential equations is established via Banach fixed-point analysis approach and using the fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in E_N.     

Existence and uniqueness results for large solutions of general nonlinear elliptic equations

We study under what condition there exists a solution of -u+f(u)=0 in a domain which blows-up on the boundary, independently of the regularity of the boundary, and we provide criteria for uniqueness. We apply our results to the case f(u)= e^au.     

Existence and uniqueness of positive solutions of a system of nonlinear algebraic equations

In this paper we consider the nonlinear system \(\gamma _i(x_i)=\sum _{j=1}^{m}g_{ij} (x_j)\), \( 1\le i \le m\). We give sufficient conditions which imply the existence and uniqueness of positive solutions of the system. Our theorem extends earlier results known in the literature. Several examples illustrate the main result.