Keywords: Upper and lower solutions p-Laplacian operator Fractional differential equation Integral boundary condition Eigenvalue a b s t r a c t In this paper, we are concerned with the eigenvalue problem of a class of singular p-Lapla-cian fractional differential equations involving the Riemann–Stieltjes integral boundary condition. The conditions for the existence of at least one positive sol...

This article developed a new result on the eigenvalue distribution for a certain class of time delay systems based on the extension of the Hermite-Biehler Theorem. Such result is applied to proportional-integral (PI) controller parameter design for a first-order plant with time delay via eigenvalue assignment. Using the method provided in this paper, one can assign the rightmost eigenvalues of ...

In this paper, we consider the eigenvalue problems for fourth order integral boundary value problems on time scales for an increasing homeomorphism and homomorphism with sign changing nonlinearities. By using a fixed point index theorem, we give the existence of eigenvalue intervals in which there exist one symmetric positive solution to the problem. An example is also given to demonstrate the ...

This work is concerned with numerical methods for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In particular, we focus on eigenvalue problems for which the evaluation of the matrix valued function is computationally expensive. Such problems arise, e.g., from boundary integral formulations of elliptic PDE-eigenvalue problems and typically exclude the use of establis...

We analyze the Ritz–Galerkin method for symmetric eigenvalue problems and prove a priori eigenvalue error estimates. For a simple eigenvalue, we prove an error estimate that depends mainly on the approximability of the corresponding eigenfunction and provide explicit values for all constants. For a multiple eigenvalue we prove, in addition, apparently the first truly a priori error estimates th...

The computational efficiency of random field representations with the Karhunen-Loève expansion relies on the numerical solution of a Fredholm integral eigenvalue problem. In this contribution, different methods for this task are compared. These include the finite element method (FEM), the finite cell method (FCM) and the Nyström method. For the FEM with linear basis functions, two different app...

In this paper, we consider some initial-boundary value problems which contain one-dimensional heat equation in non-classical case. For this problem, we can not use the classical methods such as Fourier, Laplace transformation and Fourier-Birkhoff methods. Because the eigenvalues of their spectral problems are not strictly and they are repeated or we have no eigenvalue. The presentation of the s...

This paper is concerned with solving large-scale eigenvalue problems by algebraic sub-structuring and contour integral. We combine Algebraic Sub-structuring (AS) method and the Contour Integral Rayleigh-Ritz (CIRR) method. The AS method calculates approximate eigenpairs fast and has been shown to be efficient for vibration and acoustic analysis. However, the application areas of this method hav...

In this work, we present an algorithm that enables computation of inertial modes and their corresponding frequencies in a rotating triaxial ellipsoid. The method consists of projecting the inertial mode equation onto finite-dimensional bases of polynomial vector fields. It is shown that this leads to a well-posed eigenvalue problem, and hence, that eigenmodes are of polynomial form. Furthermore...