In this paper, by Leggett-William fixed point theorem, we establish the existence of triple positive solutions of a new kind of integral boundary value problem for the nonlinear singular differential equations with p-Laplacian operator, in which q(t) can be singular at t = 0, 1. We also show that the results obtained can be applied to study certain higher order mixed boundary value problems. At...

In this article, by using the spectral analysis of the relevant linear operator and Gelfand’s formula, some properties of the first eigenvalue of a fractional differential equation are obtained. Based on these properties and through the fixed point index theory, the singular nonlinear fractional differential equations with Riemann–Stieltjes integral boundary conditions involving fractional deri...

We study the strongly singular volume integral equation that describes the scattering of time-harmonic electromagnetic waves by a penetrable obstacle. We consider the case of a cylindrical obstacle and fields invariant along the axis of the cylinder, which allows the reduction to two-dimensional problems. With this simplification, we can refine the analysis of the essential spectrum of the volu...

In this work, we prove the existence of a spectral function for singular q-Sturm-Liouville operator. Further, we establish a Parseval equality and expansion formula in eigenfunctions by terms of the spectral function.

A Tb Theorem is a boundedness criterion for singular integrals, which allows the L2 boundedness of a singular integral operator T to be deduced from sufficiently good behavior of T on some suitable non-degenerate test function b. However, in some PDE applications, including, for example, the solution of the Kato problem for square roots of divergence form elliptic operators, it may be easier to...

The space CMO of functions of finite central mean oscillation is an analogue of BMO where the condition that the sharp maximal function is bounded is replaced by the convergence of the sharp function at the origin. In this paper it is shown that each element of CMO is a singular integral image of an element of the Beurling space B2 of functions whose Hardy-Littlewood maximal function converges ...

Necessary and sufficient conditions for Calderon-Zygmund singular integral operators to be bounded operators on //' (R2) are investigated. Let m be a bounded measurable function on the circle, extended to R2 by homogeneity (m(rx) = m(x)). If the Calderon-Zygmund singular integral operator Tm , defined by Tmf = y_1C"^"(/)), is bounded on //'(R2), then it is proved that S'm has bounded variation ...

Singular and hypersingular operators are ubiquitous in problems of physics, and their use requires a careful numerical interpretation. Although analytical methods for their regularization have long been known, the classical approach does not provide numerical procedures for constructing or applying the regularized operator. We present a multiresolution definition of regularization for integral ...