共查询到20条相似文献,搜索用时 15 毫秒
1.
By means of critical point theory, existence theorems for nontrivial solutions to the Hammerstein equation x = KFx are given, where K is a compact linear integral operator and F is a nonlinear superposition operator. To this end, appropriate conditions on the spectrum of the linear parte are combined with growth and representation conditions on the nonlinear part to ensure the applicability of the mountain — pass lemma. The abstract existence theorems are applied to nonlinear elliptic equations and systems subject to Dirichlet boundary conditions. 相似文献
2.
The problem of almost everywhere stability of a nonlinear autonomous ordinary differential equation is studied using a linear transfer operator framework. The infinitesimal generator of a linear transfer operator (Perron-Frobenius) is used to provide stability conditions of an autonomous ordinary differential equation. It is shown that almost everywhere uniform stability of a nonlinear differential equation, is equivalent to the existence of a non-negative solution for a steady state advection type linear partial differential equation. We refer to this non-negative solution, verifying almost everywhere global stability, as Lyapunov density. A numerical method using finite element techniques is used for the computation of Lyapunov density. 相似文献
3.
G. Adomian 《Journal of Computational and Applied Mathematics》1984,11(3):379-380
The author's decomposition method using his An polynomials for the nonlinearities has been shown to apply to wide classes of nonlinear (or nonlinear stochastic) operator equations providing a computable, accurate solution which converges rapidly. In computation the above is sufficient for a rapid test of convergence region. 相似文献
4.
O. V. Solonukha 《Proceedings of the Steklov Institute of Mathematics》2013,283(1):226-244
An essentially nonlinear differential-difference equation containing the product of the p-Laplacian and a difference operator is considered. Sufficient conditions are obtained for the corresponding nonlinear differential-difference operator to be coercive and pseudomonotone in the case of nonvariational statement of the differential equation. The existence of a generalized solution to the Dirichlet problem for the nonlinear equation is proved. 相似文献
5.
G.W Reddien 《Journal of Mathematical Analysis and Applications》1977,60(1):139-149
Projection methods applied to abstract problems of the form Ax = Nx, where A is a linear operator with a nontrivial null space and N is a nonlinear operator, both on a normed space, are studied. Convergence results are obtained and then are applied to periodic two-point boundary value problems using splines as approximations. 相似文献
6.
We study a projection-difference method of solving the Cauchy problem for an operatordifferential equation with a selfadjoint leading operator A(t) and a nonlinear monotone subordinate operator K(·) in a Hilbert space. This method leads to a solution of a system of linear algebraic equations at each time level. Error estimates are derived for approximate solutions as well as for fractional powers of the operator A(t). The method is applied to a model parabolic problem. 相似文献
7.
We consider nonlinear boundary value problems of the type for the existence of solutions. It is assumed that L is a 2nth-order linear differential operator in the real Hilbert space S = L2[a, b] which admits a decomposition of the form where T is an nth-order linear differential operator and N is a nonlinear operator defined on a subspace of S. The decomposition of L induces a natural decomposition of the generalized inverse of L. Using the method of “alternative problems,” we split the boundary value problem into an equivalent system of two equations. The theory of monotone operators and the theory of nonlinear Hammerstein equations are then utilized to consider the solvability of the equivalent system. 相似文献
8.
Heng-you Lan Yi-shun CuiYu Fu 《Communications in Nonlinear Science & Numerical Simulation》2012,17(4):1844-1851
In this paper, we consider and study a class of general nonlinear operator inclusion couples involving (A, η, m)-resolvent operators and relaxed cocoercive type operators in Hilbert spaces. We also construct a new perturbed iterative algorithm framework with errors and investigate variational graph convergence analysis for this algorithm framework in the context of solving the nonlinear operator inclusion couple along with some results on the resolvent operator corresponding to (A, η, m)-maximal monotonicity. The obtained results improve and generalize some well known results in recent literatures. 相似文献
9.
This paper deals with the existence and multiplicity of weak solutions to nonlinear differential equations involving a general p-biharmonic operator (in particular, p-biharmonic operator) under Dirichlet boundary conditions or Navier boundary conditions. Our method is mainly based on variational arguments. 相似文献
10.
We consider discretized Hamiltonian PDEs associated with a Hamiltonian function that can be split into a linear unbounded operator and a regular nonlinear part. We consider splitting methods associated with this decomposition. Using a finite-dimensional Birkhoff normal form result, we show the almost preservation of the actions of the numerical solution associated with the splitting method over arbitrary long time and for asymptotically large level of space approximation, provided the Sobolev norm of the initial data is small enough. This result holds under generic non-resonance conditions on the frequencies of the linear operator and on the step size. We apply these results to nonlinear Schrödinger equations as well as the nonlinear wave equation. 相似文献
11.
《Journal of Mathematical Analysis and Applications》1987,124(1):189-199
A suitable expresion of a differential operator is deduced, allowing the explicit calculation of the general term fh in the power series expansion of a function f(x, t), to be utilized for solving nonlinear differential equations. 相似文献
12.
We consider the nonlinear operator equation B(λ)x + R(x, λ) = 0 with parameter λ, which is an element of a linear normed space Λ. The linear operator B(λ) has no bounded inverse for λ = 0. The range of the operator B(0) can be nonclosed. The nonlinear operator R(x, λ) is continuous in a neighborhood of zero and R(0, 0) = 0. We obtain sufficient conditions for the existence of a continuous solution x(λ) → 0 as λ → 0 with maximal order of smallness in an open set S of the space Λ. The zero of the space Λ belongs to the boundary of the set S. The solutions are constructed by the method of successive approximations. 相似文献
13.
《Mathematical and Computer Modelling》1994,19(1):89-95
The effect of the linear operator L, used in the Adomian's method for solving nonlinear partial differential equations, on the convergence is studied on the Fisher's equation, which describes a balance between linear diffusion and nonlinear reaction. The results show that the convergence of this method is not influenced by the choice of the operator L in the equation to be solved. Furthermore, under some conditions, these results are close to those obtained by using other numerical techniques. 相似文献
14.
We consider a nonlinear evolution equation for complex-valued functions of a real positive time variable and a p-adic spatial variable. This equation is a non-Archimedean counterpart of the fractional porous medium equation. Developing, as a tool, an \(L^1\)-theory of Vladimirov’s p-adic fractional differentiation operator, we prove m-accretivity of the appropriate nonlinear operator, thus obtaining the existence and uniqueness of a mild solution. We give also an example of an explicit solution of the p-adic porous medium equation. 相似文献
15.
《Communications in Nonlinear Science & Numerical Simulation》2011,16(10):3923-3932
Based on the notion of general A-monotonicity, the new proximal mapping technique and Alber’s inequalities, a new class of nonlinear relaxed cocoercive operator equations with general A-monotone operators in Banach spaces is introduced and studied. Further, we also discuss the convergence and stability of a new perturbed iterative algorithm with errors for solving this class of nonlinear operator equations in Banach spaces. Since general A-monotonicity generalizes general H-monotonicity (and in turn, generalizes A-monotonicity, H-monotonicity and maximal monotonicity), our results improve and generalize the corresponding results of recent works. 相似文献
16.
A. V. Chernov 《Mathematical Notes》2010,88(1-2):262-274
For a functional operator equation in Lebesgue space, we prove a statement on the pointwise estimate of the modulus of the increment of its global (on a fixed set Π ? ? n ) solution under the variation of the control function appearing in this equation. As an auxiliary statement, we prove a generalization of Gronwall’s lemma to the case of a nonlinear operator acting in Lebesgue space. The approach used here is based onmethods from the theory of stability of existence of global solutions to Volterra operator equations. 相似文献
17.
It is known in quantitative sociodynamics that human migration in a bounded domain can be described by a nonlinear integro-partial differential equation, which is called the master equation. This equation has its origin in statistical physics. At a physical level of rigor we can formally expand the nonlinear integral operator contained in the master equation into an infinite series whose terms are nonlinear partial differential operators. The infinite series thus obtained is called the Kramers–Moyal expansion. The purpose of this paper is to give a mathematical justification of this formal expansion. 相似文献
18.
O.S Rothaus 《Journal of Functional Analysis》1981,42(1):110-120
We study the scattering theory of a conservative nonlinear one-parameter group of operators on a Hilbert space X relative to a group of linear unitary operators. Under certain hypotheses, the scattering operator carries a neighborhood of 0 in X into X. The theory is designed to apply to the semilinear Schrödinger and Klein-Gordon equations. 相似文献
19.
Chengbo Zhai Douglas R. Anderson 《Journal of Mathematical Analysis and Applications》2011,375(2):388-400
This paper is concerned with an operator equation Ax+Bx+Cx=x on ordered Banach spaces, where A is an increasing α-concave operator, B is an increasing sub-homogeneous operator and C is a homogeneous operator. The existence and uniqueness of its positive solutions is obtained by using the properties of cones and a fixed point theorem for increasing general β-concave operators. As applications, we utilize the fixed point theorems obtained in this paper to study the existence and uniqueness of positive solutions for two classes nonlinear problems which include fourth-order two-point boundary value problems for elastic beam equations and elliptic value problems for Lane-Emden-Fowler equations. 相似文献
20.
S.K. Parhi 《Journal of Mathematical Analysis and Applications》2009,359(2):642-652
This paper deals with a third order Stirling-like method used for finding fixed points of nonlinear operator equations in Banach spaces. The semilocal convergence of the method is established by using recurrence relations under the assumption that the first Fréchet derivative of the involved operator satisfies the Hölder continuity condition. A theorem is given to establish the error bounds and the existence and uniqueness regions for fixed points. The R-order of the method is also shown to be equal to at least (2p+1) for p∈(0,1]. The efficacy of our approach is shown by solving three nonlinear elementary scalar functions and two nonlinear integral equations by using both Stirling-like method and Newton-like method. It is observed that our convergence analysis is more effective and give better results. 相似文献