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Recent research confirms that slip of a fluid on the solid surface occurs at micrometer scale. Slip on solid surface may cause the change of interior material deformation which consequently leads to the change of velocity profile and stress field. This paper concerns the time periodic electroosmotic flow in a channel with slip boundary driven by an alternating electric field, which arises from the study of particle manipulation and separation such as flow pumping and mixing enhancement. Although exact solutions to various flow problems of electroosmotic flows under the no-slip condition have been obtained, exact solutions for problems under slip boundary conditions have seldom been addressed. In this paper, an exact solution is derived for the time periodic electroosmotic flow in two-dimensional straight channels under slip boundary conditions. [ABSTRACT FROM AUTHOR]

A four-point coupled boundary value problem of fractional differential equations is studied. Based on Mawhin's coincidence degree theory, some existence theorems are obtained in the case of resonance. [ABSTRACT FROM AUTHOR]

We study the slip flow of fluids driven by the combined effect of electrical force and pressure gradient. The underlying boundary value problem is solved through the use of Fourier series expansion in time and Bessel function in space. The exact solutions and numerical investigations show that the slip length and electrical field parameters have significant effects on the velocity profile. By varying these system parameters, one can achieve smooth velocity profiles or wave form profiles with different wave amplitude and frequency. This opens the way for optimizing the flow by choosing the slip length, the electrical field, and electrolyte solutions. [ABSTRACT FROM AUTHOR]

By using the cone theory and the Banach contraction mapping principle, the existence and uniqueness results are established for nonlinear higher-order differential equation boundary value problemswith sign-changingGreen's function. The theorems obtained are very general and complement previous known results. [ABSTRACT FROM AUTHOR]

This paper provides sufficient conditions for the existence and uniqueness of positive solutions to a singular differential system with integral boundary value. The emphasis here is that the boundary conditions are coupled and this is where the main novelty of this work lies. By mixed monotone method, the existence and uniqueness results of the problem are established. An example is given to demonstrate the main results. [ABSTRACT FROM AUTHOR]

This paper investigates the existence of positive solutions for a class of singular p-Laplacian fourth- order differential equations with integral boundary conditions. By using the fixed point theory in cones, explicit range for λ and μ is derived such that for any λ and μ lie in their respective interval, the existence of at least one positive solution to the boundary value system is guaranteed. [ABSTRACT FROM AUTHOR]

We study the existence of positive solutions for the nonlinear four-point singular boundary value problem with higher-order p-Laplacian dynamic delay differential equations on time scales, subject to some boundary conditions. By using the fixed-point index theory, the existence of positive solution and many positive solutions for nonlinear four-point singular boundary value problem with p-Laplacian operator are obtained. [ABSTRACT FROM AUTHOR]

Let T be a time scale. We study the existence of positive solutions for the nonlinear four-point singular boundary value problem with p-Laplacian dynamic delay differential equations on time scales, subject to some boundary conditions. By using the fixed-point index theory, the existence of positive solution and many positive solutions for nonlinear four-point singular boundary value problem with p-Laplacian operator is obtained. [ABSTRACT FROM AUTHOR]

By employing a well-known fixed point theorem, we establish the existence of multiple positive solutions for the following fourth-order singular differential equation Lu = p(t)f(t, u(t), u"(t)) - g(t, u(t), u"(t)), 0 < t < 1, a₁u(0) - ß₁u'(0) = 0, ?₁u(1) + d₁u'(1) = 0, a₂u"(0) - ß₂u'''(0) = 0, ?₂u"(1) + d2u'''(1) = 0, with ai, ßi, ?i, di = 0 and ßi?i + ai?i + aidi > 0, i = 1, 2, where L denotes the linear operator Lu := (ru''')' - qu", r ∊ C¹([0, 1], (0, +8)), and q ∊ C([0, 1], [0, +8)). This equation is viewed as a perturbation of the fourth-order Sturm-Liouville problem, where the perturbed term g : (0, 1) × [0, +8) × (-8, +8) →(-8, +8) only satisfies the global Carathéodory conditions, which implies that the perturbed effect of g on f is quite large so that the nonlinearity can tend to negative infinity at some singular points. [ABSTRACT FROM AUTHOR]

We consider the existence of positive solutions for a class of nonlinear integral boundary value problems for fractional differential equations. By using some fixed point theorems, the existence and multiplicity results of positive solutions are obtained. The results obtained in this paper improve and generalize some well-known results. [ABSTRACT FROM AUTHOR]

By means of the fixed point theory in cones, we investigate the existence of positive solutions for the following second-order singular differential equations with a negatively perturbed term: ... where λ > 0 is a parameter; f : (0, 1) × (0,∞) →[0,∞) is continuous; f(t, x) may be singular at t = 0, t = 1, and x = 0, and the perturbed term q : (0, 1) ∞ [0, +∞) is Lebesgue integrable and may have finitely many singularities in (0, 1), which implies that the nonlinear term may change sign. [ABSTRACT FROM AUTHOR]

We consider the existence of single and multiple positive solutions for a second-order Sturm- Liouville boundary value problem in a Banach space. The sufficient condition for the existence of positive solution is obtained by the fixed point theorem of strict set contraction operators in the frame of the ODE technique. Our results significantly extend and improve many known results including singular and nonsingular cases. [ABSTRACT FROM AUTHOR]

By establishing a maximal principle and constructing upper and lower solutions, the existence of positive solutions for the eigenvalue problem of a class of fractional differential equations is discussed. Some sufficient conditions for the existence of positive solutions are established. [ABSTRACT FROM AUTHOR]

We discuss the existence of positive solutions to the following fractional m-point boundary valueproblem with changing sign nonlinearity D0+au(t) + λf(t,u(t)) = 0,0 < t < 1,u(0) = 0,D0+βu(1) =Σi=1m-2ηiD 0+ βu(ξi), where λ is a positive parameter, 1 < α ≤ 2, 0 < β < α -1, 0 < ξ 1 < • • • < ξm-2 < 1 with Σi=1m-2 ηiξiα-β-1 < 1, D0+a is the standard Riemann-Liouville derivative, f and may be singular at t = 0 and/or t = 1 and also may change sign. The work improves and generalizes some previous results. [ABSTRACT FROM AUTHOR]