Existence of Positive Solutions for Systems of Second-order Nonlinear Singular Differential Equations with Integral Boundary Conditions on Infinite Interval

By using cone theory and the Monch fixed theorem combined with a monotone iterative technique,we investigate the existence of positive solutions for systems of secondorder nonlinear singular differential equations with integral boundary conditions on infinite interval and establish the existence theorem of positive solutions and iterative sequence for approximating the positive solutions.The results in this paper improve some known results.

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-SEPARATED TYPE INTEGRAL BOUNDARY CONDITIONS

In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q （1 〈 q 〈 2） with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.

Singularly perturbed first-order differential equations with integral boundary condition

In this paper, a kind of singularly perturbed first-order differential equations with integral boundary condition are considered. With the method of boundary layer function and the Banach fixed-point theorem, the uniformly valid asymptotic solution of the original problem is obtained.

Existence of Solutions to a p-Laplacian Equation with Integral Initial Condition

In this paper, a class of one-dimension p-Laplacian equation with nonlocal initial value is studied. The existence of solutions to such a problem is obtained by using the topological degree method.

Sliding Mode Control of Coupled Tank Systems Using Conditional Integrators

For the problem of set point regulation of the liquid level in coupled tank systems, we present a continuous sliding mode control(SMC) with a "conditional integrator", which only provides integral action inside the boundary layer. For a special choice of the controller parameters, our design can be viewed as a PID controller with anti-windup and achieves robust regulation.The proposed controller recovers the transient response performance without control chattering. Both full-state feedback as well as output-feedback designs are presented in this work. Our output-feedback design uses a high-gain observer(HGO) which recovers the performance of a state-feedback design where plant parameters are assumed to be known. We consider both interacting as well as non-interacting tanks and analytical results for stability and transient performance are presented in both the cases. The proposed controller continuous SMC with conditional integrators(CSMCCI) provides superior results in terms of the performance measures as well as performance indices than ideal SMC, continuous SMC(CSMC) and continuous SMC with conventional integrator(CSMCI). Experimental results demonstrate good tracking performance in spite of unmodeled dynamics and disturbances.

Discrete Quantum Transitions, Duality: Emergence of Physical Structures and Occurrence of Observed Formations (Hidden Properties of Mathematical Physics Equations)

With the help of skew-symmetric differential forms, the hidden properties of the mathematical physics equations that describe discrete quantum transitions and emergence the physical structures are investigated. It is shown that the mathematical physics equations possess a unique property. They can describe discrete quantum transitions, emergence of physical structures and occurrence observed formations. However, such a property possesses only equations on which no additional conditions, namely, the conditions of integrability, are imposed. The intergrability conditions are realized from the equations themselves. Just under realization of integrability conditions double solutions to the mathematical physics equations, which describe discrete transitions and so on, are obtained. The peculiarity consists in the fact that the integrability conditions do not directly follow from the mathematical physics equations;they are realized under the description of evolutionary process. The hidden properties of differential equations were discovered when studying the integrability of differential equations of mathematical physics that depends on the consistence between the derivatives in differential equations along different directions and on the consistence of equations in the set of equations. The results of this work were obtained with the help of skew-symmetric differential forms that possess a nontraditional mathematical apparatus such as nonidentical relations, degenerate transformations and the transition from nonintegrable manifolds to integrable structures. Such results show that mathematical physics equations can describe quantum processes.

Driving force coordinated control of an 8x8 in-wheel motor drive vehicle with tire-road friction coefficient identification

Because of the complexities of tire-road interaction,the wheels of a multi-wheel distributed electricdrive vehicle can easily slip under certain working conditions.As wheel slip affects the dynamic per-formance and stability of the vehicle,it is crucial to control it and coordinate the driving force.With this aim,this paper presents a driving force coordination control strategy with road identification for eight-wheeled electric vehicles equipped with an in-wheel motor for each wheel.In the proposed control strategy,the road identification module estimates tire-road forces using an unscented Kalman filter al-gorithm and recognizes the road adhesion coefficient by employing the recursive least-square method According to road identification,the optimal sip ratio under the current driving condition is obtainedand a controller based on sliding mode control with a conditional integrator uses this value for accel-eration slip regulation.The anti-slip controller obtains the adjusting torque,which is integrated with the driver-command-based feedforward control torque to implement driving force coordination control.The results of hardware-in-loop simulation show that this control strategy can accurately estimate tire-roadrces as well as the friction coefficient,and thus,can effectively fulfill the purpose of driving force coordinated control under different driving conditions.

SOLUTION OF DIFFERENT HOLES SHAPE BORDERS OF FIBRE REINFORCED COMPOSITE PLATES BY INTEGRAL EQUATIONS

Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.

Solvability of the Nonlocal Inverse Parabolic Problem and Numerical Results

In this paper,we consider the unique solvability of the inverse problem of determining the right-hand side of a parabolic equation whose leading coefficient depends on time variable under nonlocal integral overdetermination condition.We obtain sufficient conditions for the unique solvability of the inverse problem.The existence and uniqueness of the solution of the inverse parabolic problem upon the data are established using the fixed point theorem.This inverse problem appears extensively in the modelling of various phenomena in engineering and physics.For example,seismology,medicine,fusion welding,continuous casting,metallurgy,aircraft,oil and gas production during drilling and operation of wells.In addition,the numerical solution of the inverse problem is studied by using the Crank-Nicolson finite difference method together with the Tikhonov regularization to find a stable and accurate approximate solution of finite differences.The resulting nonlinear system of parabolic equation is solved computationally using the MATLAB subroutine lsqnonlin.Both analytical and numerically simulated noisy input data are inverted.The root mean square error values for various noise levels for both continuous and discontinuous time-dependent heat source term are compared.Numerical results presented for two examples show the efficiency of the computational method and the accuracy and stability of the numerical solution even in the presence of noise in the input data.Furthermore,the choice of the regularization parameter is also discussed based on the trial and error technique.

Existence of Positive Solutions for Singular Fourth Order Coupled System with Sign Changing Nonlinear Terms

This paper deals with the existence of positive solutions to a singular fourth order coupled system with integral boundary conditions. Since the nonlinear terms f, g may change sign or be singular at t = 0 or t = 1, the authors make a priori estimates to overcome some difficulties and apply Cuo-Krasnoselskii fixed point theorem to prove the existence of solutions of the system under suitable assumptions. Finally, some examples to illustrate the main results are given.

New smooth gap function for box constrained variational inequalities

A new smooth gap function for the box constrained variational inequality problem （VIP） is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable properties. The box constrained VIP can be reformulated as a differentiable optimization problem by the proposed smooth gap function. The conditions, under which any stationary point of the optimization problem is the solution to the box constrained VIP, are discussed. A simple frictional contact problem is analyzed to show the applications of the smooth gap function. Finally, the numerical experiments confirm the good theoretical properties of the method.

Multiple Positive Solutions for One Dimensional Third Order p-Laplacian Equations with Integral Boundary Conditions

In this paper,we consider the one dimensional third order p-Laplacian equation(Фp(u″))′+h(t)f(t,u(t))=0 with integral boundary conditions u(0)-αu′(0)=∫_(0)^(1) g1(s)u(s)ds,u(1)+βu′(1)=∫_(0)^(1)g2(s)u(s)ds,u″(0)=0.By using kernel functions and the Avery-Peterson fixed point theorem,we establish the existence of at least three positive solutions.

POSITIVE SOLUTIONS TO A BVP WITH TWO INTEGRAL BOUNDARY CONDITIONS

Based on the Guo-Krasnoselskii’s fixed-point theorem,the existence and multiplicity of positive solutions to a boundary value problem(BVP)with two integral boundary conditions{v(4)=f(s,v(s),v′(s),v〞(s)),s∈[0,1],v′(1)=v′'′(1)=0,v(0)=∫10 g1(T)v(T )dT ,v′′(0)=∫10 g2( T)v′′(T )d T}are obtained,where f,g1,g2 are all continuous.It generalizes the results of one positive solution to multiplicity and improves some results for integral BVPs.Moreover,some examples are also included to demonstrate our results as applications.

On the General Stability of a Viscoelastic Wave Equation with an Integral Condition

We consider a nonlocal boundary value problem for a viscoelastic equation with a Bessel operator and a weighted integral condition and we prove a general decay result.We also give an example to show that our general result gives the optimal decay rate for ceratin polynomially decaying relaxation functions.This result improves some other results in the literature.

Existence of Solutions to a p-Laplacian Equation with Integral Initial Condition

In this paper, a class of one-dimension p-Laplacian equation with nonlocal initial value is studied. The existence of solutions for such a problem is obtained by using the topological degree method.

Generic conformally flat hypersurfaces and surfaces in 3-sphere

The aim of this paper is to verify that the study of generic conformally flat hypersurfaces in 4-dimensional space forms is reduced to a surface theory in the standard 3-sphere.The conformal structure of generic conformally flat(local-)hypersurfaces is characterized as conformally flat(local-)3-metrics with the Guichard condition.Then,there is a certain class of orthogonal analytic(local-)Riemannian 2-metrics with constant Gauss curvature-1 such that any 2-metric of the class gives rise to a one-parameter family of conformally flat 3-metrics with the Guichard condition.In this paper,we firstly relate 2-metrics of the class to surfaces in the 3-sphere:for a 2-metric of the class,a 5-dimensional set of(non-isometric)analytic surfaces in the 3-sphere is determined such that any surface of the set gives rise to an evolution of surfaces in the 3-sphere issuing from the surface and the evolution is the Gauss map of a generic conformally flat hypersurface in the Euclidean4-space.Secondly,we characterize analytic surfaces in the 3-sphere which give rise to generic conformally flat hypersurfaces.

Vector NLS solitons interacting with a boundary

We construct multi-soliton solutions of the n-component vector nonlinear Schrödinger equation on the half-line subject to two classes of integrable boundary conditions(BCs):the homogeneous Robin BCs and the mixed Neumann/Dirichlet BCs.The construction is based on the so-called dressing the boundary,which generates soliton solutions by preserving the integrable BCs at each step of the Darboux-dressing process.Under the Robin BCs,examples,including boundary-bound solitons,are explicitly derived;under the mixed Neumann/Dirichlet BCs,the boundary can act as a polarizer that tunes different components of the vector solitons.Connection of our construction to the inverse scattering transform is also provided.

MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF INTEGRAL BOUNDARY VALUE PROBLEM

In this paper,the existence and multiplicity of positive solutions for a class of non-resonant fourth-order integral boundary value problem{u(4)(t)+βu″(t)-au(t)=f(t,u(t),u″(t)),t∈(0,1),u″(0)=u″(1)=0,u(0)=0,u(1)=(1/λ2-1/λ1)∫01q(s)f(s,u(s),u″(s))ds with two parameters are established by using the Guo-Krasnoselskii's fixedpoint theorem,where f∈C([0,1]×[0,+∞)×(-∞,0],[0,+∞)),q(t)∈L1[0,1]is nonnegative,α,β∈R and satisfyβ<2π2,α>0,α/π4+β/π2<1,λ1,2=(-β+√β^2+4a)/2.The corresponding examples are raised to demonstrate the results we obtained.

Parametrized Area Integrals on Hardy Spaces and Weak Hardy Spaces

In this paper, the authors prove that if Ω satisfies a class of the integral Dini condition, then the parametrized area integral μΩ,S^ρ is a bounded operator from the Hardy space H1 （R^n） to L1 （R^n） and from the weak Hardy space H^1,∞ （R^n） to L^1,∞ （R^n）, respectively. As corollaries of the above results, it is shown that μΩ,S^ρ is also an operator of weak type These conclusions are substantial improvement and （1, 1） and of type （p,p） for 1 〈 p 〈 2, respectively extension of some known results.