Related papers: Generalized eigenvalues for fully tnonlinear singu…
In this paper we extend existing results concerning generalized eigenvalues of Pucci's extremal operators. In the radial case, we also give a complete description of their spectrum, together with an equivalent of Rabinowitz's Global…
This paper is devoted to the proof of the existence of the principal eigenvalue and related eigenfunctions for fully nonlinear degenerate or singular uniformly elliptic equations posed in a punctured ball, in presence of a singular…
We study the generalized eigenvalue problem on the whole space for a class of integro-differential elliptic operators. The nonlocal operator is over a finite measure, but this has no particular structure. Some of our results even hold for…
We study an eigenvalue problem involving a degenerate and singular elliptic operator on the whole space $\mathbb{R}^N$. We prove the existence of an unbounded and increasing sequence of eigenvalues. Our study generalizes to the case of…
In this paper we present an elementary theory about the existence of eigenvalues for fully nonlinear radially symmetric 1-homogeneous operators. A general theory for first eigenvalues and eigenfunctions of 1-homogeneous fully nonlinear…
We study the generalized eigenvalue problem in $\mathbb{R}^N$ for a general convex nonlinear elliptic operator which is locally elliptic and positively $1$-homogeneous. Generalizing article of Berestycki and Rossi in [Comm. Pure Appl. Math.…
In this article we prove some Lipschitz estimates and existence result for a class of degenerate fully nonlinear elliptic equations which are a generalization of the pseudo p-Laplacian. The operators are degenerate elliptic at any point…
Through the Maximum principle we define the principal eigenvalue for a class of fully-nonlinear operators that are the non-variational equivalent of the p-Laplacian. We also obtain some a priori Holder estimates for non-negative solutions…
In this work, we review and extend some well known results for the eigenvalues of the Dirichlet $p-$Laplace operator to a more general class of monotone quasilinear elliptic operators. As an application we obtain some homogenization results…
In this paper we study the maximum principle, the existence of eigenvalue and the existence of solution for the Dirichlet problem for operators which are fully-nonlinear, elliptic but presenting some singularity or degeneracy which are…
In this paper we introduce some fully nonlinear second order operators defined as weighted partial sums of the eigenvalues of the Hessian matrix, arising in geometrical contexts, with the aim to extend maximum principles and removable…
In this paper we prove existence of (viscosity) solutions of Dirichlet problems concerning fully nonlinear elliptic operator, which are either degenerate or singular when the gradient of the solution is zero. For this class of operators it…
We prove the backward uniqueness for general parabolic operators of second order in the whole space under assumptions that the leading coefficients of the operator are Lipschitz and their gradients satisfy certain decay conditions. This…
In this chapter we are examining several iterative methods for solving nonlinear eigenvalue problems. These arise in variational image-processing, graph partition and classification, nonlinear physics and more. The canonical eigenproblem we…
This paper is devoted to the proof of the existence of the principal eigenvalue and related eigenfunctions for fully nonlinear uniformly elliptic equations posed in a punctured ball, in presence of a singular potential. More precisely, we…
The notions of generalized principal eigenvalue for linear second order elliptic operators in general domains introduced by Berestycki et al. \cite{BNV,BR0,BR3} have become a very useful and important tool in analysis of partial…
In this paper we partially settle our conjecture from [1] (math.SP/0701143) on roots of eigenpolynomials for degenerate exactly-solvable operators. Namely, for any such operator, we establish a lower bound (which supports our conjecture)…
In this paper we consider generalized eigenvalue problems for a family of operators with a polynomial dependence on a complex parameter. This problem is equivalent to a genuine non self-adjoint operator. We discuss here existence of non…
Using three different notions of generalized principal eigenvalue of linear second order elliptic operators in unbounded domains, we derive necessary and sufficient conditions for the validity of the maximum principle, as well as for the…
We consider fourth order ordinary differential operator with compactly supported coefficients on the line. We determine asymptotics of the number of resonances in complex discs at large radius. We consider resonances of an Euler-Bernoulli…