A numerical method for solving the problem
A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix
It is shown that if A is a bounded linear operator on a complex Hilbert space, then , where w(A) and ||A|| are the numerical radius and the usual operator norm of A, respectively. An application of this inequality is given to obtain a new estimate for the numerical radius of the Frobenius companion matrix. Bounds for the zeros of polynomials are also given.
A numerical radius inequality involving the generalized Aluthge transform
A spectral radius inequality is given. An application of this inequality to prove a numerical radius inequality that involves the generalized Aluthge transform is also provided. Our results improve earlier results by Kittaneh and Yamazaki.
A one dimensional Hammerstein problem.
A -Laplacian system with resonance and nonlinear boundary conditions on an unbounded domain
We study a nonlinear elliptic system with resonance part and nonlinear boundary conditions on an unbounded domain. Our approach is variational and is based on the well known Landesman-Laser type conditions.
A pair of non-self mappings in cone metric spaces
A Paley-Wiener type theorem for generalized non-quasianalytic classes
Let P be a hypoelliptic polynomial. We consider classes of ultradifferentiable functions with respect to the iterates of the partial differential operator P(D) and prove that such classes satisfy a Paley-Wiener type theorem. These classes and the corresponding test spaces are nuclear.
A parabolic - elliptic variational inequality.
A parabolic quasilinear problem for linear growth functionals.
We prove existence and uniqueness of solutions for the Dirichlet problem for quasilinear parabolic equations in divergent form for which the energy functional has linear growth.
A parameter choice for Tikhonov regularization for solving nonlinear inverse problems leading to optimal convergence rates
We give a derivation of an a-posteriori strategy for choosing the regularization parameter in Tikhonov regularization for solving nonlinear ill-posed problems, which leads to optimal convergence rates. This strategy requires a special stability estimate for the regularized solutions. A new proof fot this stability estimate is given.
A partial differential operator which is surjective on Gevrey classes with 1 ≤ d < 2 and d ≥ 6 but not for 2 ≤ d < 6
It is shown that the partial differential operator is surjective if 1 ≤ d < 2 or d ≥ 6 and not surjective for 2 ≤ d < 6.
A penalty approach for a box constrained variational inequality problem
We propose a penalty approach for a box constrained variational inequality problem . This problem is replaced by a sequence of nonlinear equations containing a penalty term. We show that if the penalty parameter tends to infinity, the solution of this sequence converges to that of when the function involved is continuous and strongly monotone and the box contains the origin. We develop the algorithmic aspect with theoretical arguments properly established. The numerical results tested on...
A periodic boundary value problem in Hilbert space
In the paper some existence results for periodic boundary value problems for the ordinary differential equation of the second order in a Hilbert space are given. Under some auxiliary assumptions the set of solutions is compact and connected or it is convex.
A perspective on the contributions of Alan C. Lazer to critical point theory.
A perturbation characterization of compactness of self-adjoint operators
A characterization of compactness of a given self-adjoint bounded operator A on a separable infinite-dimensional Hilbert space is established in terms of the spectrum of perturbations. An example is presented to show that without separability, the perturbation condition, which is always necessary, is not sufficient. For non-separable spaces, another condition on the self-adjoint operator A, which is necessary and sufficient for the perturbation, is given.
A perturbation of Lomonosov's theorem
A perturbation problem in the presence of affine symmetries
An approach to a local analysis of solutions of a perturbation problem is proposed when the unperturbed operator has affine symmetries. The main result is a local theorem on existence, uniqueness, and analytic dependence on a parameter.
A perturbation theorem for semigroups of linear operators
A Perturbation Theorem for the Essential Spectral Radius of Strongly Continuous Semigroups.
A perturbation theory of resonances