共查询到20条相似文献,搜索用时 15 毫秒
1.
This paper investigates the existence of positive solutions of singular multi-point boundary value problems of fourth order ordinary differential equation with p-Laplacian. A necessary and sufficient condition for the existence of C2[0,1] positive solution as well as pseudo-C3[0,1] positive solution is given by means of the fixed point theorems on cones. 相似文献
2.
In this paper, we study the existence and multiplicity of classical solutions for a second-order impulsive differential equation with periodic boundary conditions. By using a variational method and critical point theory, we give some new criteria to guarantee that the impulsive problem has at least one solution, two solutions and infinitely many solutions when the parameter pair (c,λ) lies in different intervals, respectively. Some examples are given in this paper to illustrate the main results. 相似文献
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4.
This work investigates the existence of monotonic traveling wave and standing wave solutions of RTD-based cellular neural networks in the one-dimensional integer lattice . For nonzero wave speed c, applying the monotone iteration method with the aid of real roots of the corresponding characteristic function of the profile equation, we can partition the parameter space (γ,δ)-plane into four regions such that all the admissible monotonic traveling wave solutions connecting two neighboring equilibria can be classified completely. For the case of c=0, a discrete version of the monotone iteration scheme is established for proving the existence of monotonic standing wave solutions. Furthermore, if γ or δ is zero then the profile equation for the standing waves can be viewed as an one-dimensional iteration map and we then prove the multiplicity results of monotonic standing waves by using the techniques of dynamical systems for maps. Some numerical results of the monotone iteration scheme for traveling wave solutions are also presented. 相似文献
5.
Aiping Wang 《Journal of Differential Equations》2009,246(4):1600-1644
The GKN (Glazman, Krein, Naimark) Theorem characterizes all self-adjoint realizations of linear symmetric (formally self-adjoint) ordinary differential equations in terms of maximal domain functions. These functions depend on the coefficients and this dependence is implicit and complicated. In the regular case an explicit characterization in terms of two-point boundary conditions can be given. In the singular case when the deficiency index d is maximal the GKN characterization can be made more explicit by replacing the maximal domain functions by a solution basis for any real or complex value of the spectral parameter λ. In the much more difficult intermediate cases, not all solutions contribute to the singular self-adjoint conditions. In 1986 Sun found a representation of the self-adjoint singular conditions in terms of certain solutions for nonreal values of λ. In this paper we give a representation in terms of certain solutions for real λ. This leads to a classification of solutions as limit-point (LP) or limit-circle (LC) in analogy with the celebrated Weyl classification in the second-order case. The LC solutions contribute to the singular boundary conditions, the LP solutions do not. The advantage of using real λ is not only because it is, in general, easier to find explicit solutions but, more importantly, it yields information about the spectrum. 相似文献
6.
Ricardo Enguiça 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(9):2968-2979
We start by studying the existence of positive solutions for the differential equation
u″=a(x)u−g(u), 相似文献
7.
Francesca Dalbono Walter Dambrosio 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(7):2720-2738
We prove the existence of a double infinite sequence of radial solutions for a Dirichlet concave-convex problem associated with an elliptic equation in a ball of Rn. We are interested in relaxing the classical positivity condition on the weights, by allowing the weights to vanish. The idea is to develop a topological method and to use the concept of rotation number. The solutions are characterized by their nodal properties. 相似文献
8.
We study the nonlinear boundary value problem consisting of the equation y″+w(t)f(y)=0 on [a,b] and a multi-point boundary condition. By relating it to the eigenvalues of a linear Sturm-Liouville problem with a two-point separated boundary condition, we obtain results on the existence and nonexistence of nodal solutions of this problem. We also discuss the changes in the existence question for different types of nodal solutions as the problem changes. 相似文献
9.
Shouchuan Hu Nikolas S. Papageorgiou 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(12):3675-883
We consider a nonlinear periodic equation driven by the scalar p-Laplacian and with a Caratheodory asymptotically (p−1)-linear nonlinearity. Using variational methods coupled with suitable truncation techniques, we show that the problem has at least two positive solutions. For the semilinear case (p=2), using Morse theory we show that the problem has three distinct positive solutions. 相似文献
10.
Unbounded upper and lower solutions theories are established for the Sturm–Liouville boundary value problem of a second order ordinary differential equation on infinite intervals. By using such techniques and the Schäuder fixed point theorem, the existence of solutions as well as the positive ones is obtained. Nagumo conditions play an important role in the nonlinear term involved in the first-order derivatives. 相似文献
11.
Walter Dambrosio 《Journal of Differential Equations》2004,196(1):91-118
In this paper we are concerned with the existence and multiplicity of nodal solutions to the Dirichlet problem associated to the elliptic equation Δu+q(|x|)g(u)=0 in a ball or in an annulus in .The nonlinearity g has a superlinear and subcritical growth at infinity, while the weight function q is nonnegative in [0,1] and strictly positive in some interval [r1,r2]⊂[0,1].By means of a shooting approach, together with a phase-plane analysis, we are able to prove the existence of infinitely many solutions with prescribed nodal properties. 相似文献
12.
Daqing Jiang Ying Yang Jifeng Chu Donal O’Regan 《Nonlinear Analysis: Theory, Methods & Applications》2007
In this paper, we show that the monotone technique produces two monotone sequences that converge uniformly to extremal solutions of second order functional differential equations and ?-Laplacian equations with Neumann boundary value conditions. Moreover, we obtain existence results assuming upper and lower solutions in the reverse order. 相似文献
13.
Svatoslav Staněk 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):e153
The paper discusses the existence of positive and dead core solutions of the singular differential equation (?(u″))′=λf(t,u,u′,u″) satisfying the boundary conditions u(0)=A, u(T)=A, min{u(t):t∈[0,T]}=0. Here λ is a nonnegative parameter, A is a positive constant and the Carathéodory function f(t,x,y,z) is singular at the value 0 of its space variable y. 相似文献
14.
We investigate the singular Weyl-Titchmarsh m-function of perturbed spherical Schrödinger operators (also known as Bessel operators) under the assumption that the perturbation q(x) satisfies xq(x)∈L1(0,1). We show existence plus detailed properties of a fundamental system of solutions which are entire with respect to the energy parameter. Based on this we show that the singular m-function belongs to the generalized Nevanlinna class and connect our results with the theory of super singular perturbations. 相似文献
15.
Fangfei Li Mei JiaXiping Liu Chunling LiGaoshang Li 《Nonlinear Analysis: Theory, Methods & Applications》2008
This paper studies the existence and uniqueness of solutions of second-order three-point boundary value problems with lower and upper solutions in the reversed order, obtains the sufficient conditions for the existence and uniqueness of solutions by use of the monotone iterative method, and gives the iterative sequence for solving a solution and its error estimate formula under the condition of unique solution. 相似文献
16.
Boundary value problems for first order functional differential equations with impulsive integral conditions 总被引:1,自引:0,他引:1
Jessada Tariboon 《Journal of Computational and Applied Mathematics》2010,234(8):2411-2419
In this paper, by using the method of lower and upper solutions coupled with the monotone iterative technique, we give conditions for existence of extreme solutions for first order functional differential equations with a new impulsive integral condition. Some comparison results are also formulated. 相似文献
17.
By using the fixed-point principle in cone and the fixed-point index theory for strict-set-contraction operator, this paper investigates the existence, nonexistence, and multiplicity of positive solutions for a class of nonlinear three-point boundary value problems of nth-order differential equations in ordered Banach spaces. In addition, an example is included to demonstrate the main results. 相似文献
18.
《Quaestiones Mathematicae》2013,36(2):165-185
Abstract In this paper the odd-order differential equation M[y] λ wy on the interval (O,∞), associated with the symmetric differential expression M of (2k-1)st order (k ≥ 2) with w a positive weight function and λ a complex number, is shown to possess k-Titchmarsh-Weyl solutions for every non-real λ in the underlying Hilbert space L2 w(O, ∞) having identical representation for every non-real λ. In terms of these solutions the Green's function associated with the singular boundary value problem is shown to possess identical representation for all non-real λ which has been further made use of in the third-order case to establish a direct convergence eigenfunction expansion theorem. The symmetric spectral matrix appearing in the expansion theorem has been characterized in terms of the Titchmarsh-Weyl m-coefficients. 相似文献
19.
Alexander M. Krasnosel'skii Dmitrii I. Rachinskii 《Journal of Differential Equations》2006,226(1):30-53
We are concerned with a subharmonic bifurcation from infinity for scalar higher order ordinary differential equations. The equations contain principal linear parts depending on a scalar parameter, 2π-periodic forcing terms, and continuous nonlinearities with saturation. We suggest sufficient conditions for the existence of subharmonics (i.e., periodic solutions of multiple periods 2πn) with arbitrarily large amplitudes and periods. We prove that this type of the subharmonic bifurcation occurs whenever a pair of simple roots of the characteristic polynomial crosses the imaginary axis at the points ±αi with an irrational α. Under some further assumptions, we estimate asymptotically the parameter intervals, where large subharmonics of periods 2πn exist. These assumptions relate the quality of the Diophantine approximations of α, the rate of convergence of the nonlinearity to its limits at infinity, and the smoothness of the forcing term. 相似文献
20.
A singular initial value problem and self-similar solutions of a nonlinear dissipative wave equation
Jianfeng Liang 《Journal of Differential Equations》2009,246(2):819-844
We present a systematic study of local solutions of the ODE of the form near t=0. Such ODEs occur in the study of self-similar radial solutions of some second order PDEs. A general theorem of existence and uniqueness is established. It is shown that there is a dichotomy between the cases γ>0 and γ<0, where γ=∂f/∂x′ at t=0. As an application, we study the singular behavior of self-similar radial solutions of a nonlinear wave equation with superlinear damping near an incoming light cone. A smoothing effect is observed as the incoming waves are focused at the tip of the cone. 相似文献