On the kernels associated with a class of hyponormal operators

The explicit forms of a pair of mutually reciprocal analytic and hermitian kernels associated with a class of simple hyponormal operators and its relation with the unilateral shift is established.     

On a class of fractional non-selfadjoint operators associated with differential equations

We present a research method for non-selfadjoint integral operators associated with fractional differential equations. With the help of this method we, in particular, estimate eigen-functions and eigenvalues of the boundary-value problem for a fractional oscillatory equation.     

Boundedness of a class of super singular integral operators and the associated commutators

In this paper we give the (Lα p, Lp) boundedness of the maximal operator of a class of super singular integrals defined bywhich improves and extends the known result. Moreover, by applying an off-Diagonal T1 Theorem, we also obtain the (Lp, Lq) boundedness of the commutator defined by     

Iterative method for a class of fourth-order p-Laplacian beam equation

This paper considers the existence of the solutions for a class of fourth-order $p$-Laplacian. The boundary value problem considered can describe the tiny deformation of an elastic beam. By using a novel efficient iteration method, the existence and uniqueness result of solution for the problem is obtained. An example is given to illustrate the main results.     

On a class of quasi-Fredholm operators

We study a class of bounded linear operators acting on a Banach spaceX called B-Fredholm operators. Among other things we characterize a B-Fredholm operator as the direct sum of a nilpotent operator and a Fredholm operator and we prove a spectral mapping theorem for B-Fredholm operators.IMemory of my father, Sidi-Bouhouria 1914-0991.     

Estimates at infinity for positive solutions to a class of p-Laplacian problems in RN

In this paper we consider a class of logistic-type problems for the p-Laplacian in the whole space. Using minimization we prove existence of a positive solution and its behavior at infinity. We also consider questions of uniqueness and sharp estimates at infinity.     

Bifurcation diagrams in a class of Kolmogorov systems

We study a class of Kolmogorov systems of dimension two depending on two independent parameters. The local behavior of the system is described in terms of bifurcation diagrams which contain the bifurcation curves separating a node from a focus.     

On a class of singular p-Laplacian semipositone problems with sign-changing weights

We study existence of positive weak solution for a class of $p$-Laplacian problem $$\left\{\begin{array}{ll}-\Delta_{p}u = \lambda g(x)[f(u)-\frac{1}{u^{\alpha}}], & x\in \Omega,\\u= 0 , & x\in\partial \Omega,\end{array\right.$$ where $\lambda$ is a positive parameter and $\alpha\in(0,1),$ $\Omega $ is a bounded domain in $ R^{N}$ for $(N > 1)$ with smooth boundary, $\Delta_{p}u = div (|\nabla u|^{p-2}\nabla u)$ is the p-Laplacian operator for $( p > 2),$ $g(x)$ is $C^{1}$ sign-changing function such that maybe negative near the boundary and be positive in the interior and $f$ is $C^{1}$ nondecreasing function $\lim_{s\to\infty}\frac{f(s)}{s^{p-1}}=0.$ We discuss the existence of positive weak solution when $f$ and $g$ satisfy certain additional conditions. We use the method of sub-supersolution to establish our result.     

Adjoints of a class of composition operators

Adjoints of certain operators of composition type are calculated. Specifically, on the classical Hardy space of the open unit disk operators of the form are considered, where is a finite Blaschke product. is obtained as a finite linear combination of operators of the form where and are rational functions, are associated Toeplitz operators and is defined by

     

A counterexample to a lower bound for a class of pseudodifferential operators

We present a counterexample to a possible improvement of a lower bound for a class of pseudodifferential operators with symplectic characteristic manifold.