Related papers: Nonlinear Eigenvalues and Bifurcation Problems for…
We study Toeplitz operators with separately radial and radial symbols on the weighted Bergman spaces on the unit ball. The unitary equivalence of such operators with multiplication operators on $\ell^2$ spaces was previously obtained by…
In this work we establish eigenvalue inequalities for elliptic differential operators either for Dirichlet or for Robin eigenvalue problems, by using the technique introduced by Alexandroff, Bakelman and Pucci. These inequalities can be…
The dual purpose of this article is to establish bilinear Poincare-type estimates associated to an approximation of the identity and to explore the connections between bilinear pseudo-differential operators and bilinear potential-type…
In order to prove numerically the global existence and uniqueness of smooth solutions of a fourth order, nonlinear PDE, we derive rigorous a-posteriori upper bounds on the supremum of the numerical range of the linearized operator. These…
For $p \in (1, \infty),$ for an integer $N \geq 2$ and for a bounded Lipschitz domain $\Omega$, we consider the following nonlinear Steklov bifurcation problem \begin{equation*} \begin{aligned} -\Delta_p \phi & = 0 \; \text{in} \ \Omega, \\…
We introduce higher-order Poincar'e constants for compact weighted manifolds and estimate them from above in terms of subsets. These estimates imply upper bounds for eigenvalues of the weighted Laplacian and the first nontrivial eigenvalue…
In this note we devise and analyse well-posed variational formulations and operator theoretical methods for boundary value problems associated to the biharmonic operator. Of particular interest are Neumann type and over- and underdetermined…
We study a class of rotation invariant determinantal ensembles in the complex plane; examples include the eigenvalues of Gaussian random matrices and the roots of certain families of random polynomials. The main result is a criteria for a…
In the analysis of parametrized nonautonomous evolutionary equations, bounded entire solutions are natural candidates for bifurcating objects. Appropriate explicit and sufficient conditions for such branchings, however, require to combine…
We consider a nonlinear partial differential equation for complex-valued functions which is related to the two-dimensional stationary Schrodinger equation and enjoys many properties similar to those of the ordinary differential Riccati…
A generalized two-dimensional periodic Dirac operator is considered, with $L^{\infty}$-matrix-valued coefficients of the first order derivatives and with complex matrix-valued potential. It is proved that if the matrix-valued potential has…
This article proposed a new approach to the determination of the spectrum for nonlinear continuous operators in the Banach spaces and using it investigated the spectrum of some classes of operators. Here shows that in nonlinear operators…
We study radial sign-changing solutions of a class of fully nonlinear elliptic Dirichlet problems in a ball, driven by the extremal Pucci's operators and with a power nonlinear term. We first determine a new critical exponent related to the…
This paper is concerned with the Minkowski convolution of viscosity solutions of fully nonlinear parabolic equations. We adopt this convolution to compare viscosity solutions of initial-boundary value problems in different domains. As a…
Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally…
We introduce the notion of $ P -$functions for fully nonlinear equations and establish a general criterion for obtaining such quantities for this class of equations. Some applications are gradient bounds, De Giorgi-type properties of entire…
This paper provides both the theoretical results and numerical calculations of global solution curves, by continuation in global parameters. Each point on the solution curves is computed directly as the global parameter is varied, so that…
In this work, we investigate the existence of multiple positive solutions for a weakly coupled system of nonlinear elliptic equations governed by Pucci extremal operators. Specifically, we consider the system: \[ \begin{cases}…
For $s_1,s_2\in(0,1)$ and $p,q \in (1, \infty)$, we study the following nonlinear Dirichlet eigenvalue problem with parameters $\alpha, \beta \in \mathbb{R}$ driven by the sum of two nonlocal operators: \begin{equation*} (-\Delta)^{s_1}_p…
It is shown that eigenvalues of Laplace-Beltrami operators on compact Riemannian manifolds can be determined as limits of eigenvalues of certain finite-dimensional operators in spaces of polyharmonic functions with singularities. In…