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The present paper is devoted to the investigation of a parabolic equation with moving boundaries arising in ductal carcinoma in situ (DCIS) model. Approximation solution of this problem is implemented by Ritz-Galerkin, which is a first attempt at tackling such problem. In process of dealing with this moving boundary condition, we use a trick of introducing two transformations to convert moving boundary to nonclassical boundary that can be handled with Ritz-Galerkin method. Also, existence and uniqueness are proved. Illustrative examples are included to demonstrate the validity and applicability of the technique in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we study the exterior problem for the spherically symmetric isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficients. Under certain assumptions imposed on the initial data, we show that there exists a unique global strong solution to the exterior problem and obtain the regularity of the strong solution. Some ideas and more delicate estimates are introduced to prove these results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence, nonexistence, uniqueness, and multiplicity of positive solutions for a class of eigenvalue problems of nonlinear fractional differential equations with a nonlinear integral term and a disturbance parameter in the boundary conditions. By using fixed point index theory we give the critical curve of eigenvalue λ and disturbance parameter μ that divides the range of λ and μ for the existence of at least two, one, and no positive solutions for the eigenvalue problem. Furthermore, by using fixed point theorem for a sum operator with a parameter we establish the maximum eigenvalue interval for the existence of the unique positive solution for the eigenvalue problem and show that such a positive solution depends continuously on the parameter λ for given μ. In particular, we give estimates for the critical value of parameters. Two examples are given to illustrate our main results. [ABSTRACT FROM AUTHOR]

In this paper we study a class of singularly perturbed interface boundary value problems with discontinuous source terms. We first establish a lemma of lower-upper solutions by using the Schauder fixed point theorem. By the method of boundary functions and the lemma of lower-upper solutions we obtain the existence, asymptotic estimates, and uniqueness of the solution with boundary and interior layers for the proposed problem. [ABSTRACT FROM AUTHOR]

This paper investigates some nonlinear third-order ordinary differential equations and inclusions with anti-periodic type integral boundary conditions and multi-strip boundary conditions. To establish the existence results for the given problems, we apply standard tools of fixed point theory for single-valued and multi-valued problems. The results are illustrated with the aid of examples. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of positive solutions to the singular elliptic boundary value problem involving p-Laplace operator ... where Ω⊂ RN (N = 1) is a bounded domain with smooth boundary ∂ Ω, h ∈ L¹(Ω), h(x) > 0 almost everywhere in Ω, k ∈ L∞(Ω) is nonnegative, p > 2, α > 1 and ß ∈ (0, p - 1). A compatibility condition on the couple (h(x),a) is given for the problem to have at least one solution. More precisely, it is shown that the problem admits a solution if and only if there exists u0 ∈ H¹0(Ω) such that ƒΩ hu01-a 0 dx <∞. [ABSTRACT FROM AUTHOR]

We shall consider the Sturm-Liouville boundary value problem y(m)(t) + λF(t,y(t), y'(t),..., y(q)(t)) = 0, t ∈ (0, 1), y(k)(0) = 0, 0 ≤ k ≤ m- 3, ζ y(m-2)(0) - θy(m-1)(0) = 0, py(m-2)(1) + δy(m-1)(1) = 0 where m ≥ 3, 1 ≤ q ≤ m - 2, and λ > 0. It is noted that the boundary value problem considered has a derivative-dependent nonlinear term, which makes the investigation much more challenging. In this paper we shall develop a new technique to characterize the eigenvalues? so that the boundary value problem has a positive solution. Explicit eigenvalue intervals are also established. Some examples are included to dwell upon the usefulness of the results obtained. [ABSTRACT FROM AUTHOR]

In this paper, a mid-knot cubic non-polynomial spline is applied to obtain the numerical solution of a system of second-order boundary value problems. The numerical method is proved to be uniquely solvable and it is of second-order accuracy. We further include three examples to illustrate the accuracy of our method and to compare with other methods in the literature. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of infinitely many solutions for a class of impulsive fractional boundary value problems with p-Laplacian. Based on a variant fountain theorem, the existence of infinitely many nontrivial high or small energy solutions is obtained. In addition, two examples are worked out to illustrate the effectiveness of the main results. [ABSTRACT FROM AUTHOR]