Unbounded nonlinear perturbations of linear elliptic problems at resonance

Research Article Unbounded Perturbations of Nonlinear Second-Order Difference Equations at Resonance

Elliptic and parabolic problems in unbounded domains

We consider elliptic and parabolic problems in unbounded domains. We give general existence and regularity results in Besov spaces and semi-explicit representation formulas via operatorvalued fundamental solutions which turn out to be a powerful tool to derive a series of qualitative results about the solutions. We give a sample of possible applications including asymptotic behavior in the larg...

Optimal Approximation of Elliptic Problems by Linear and Nonlinear Mappings

We study the optimal approximation of the solution of an operator equation A(u) = f by linear mappings of rank n and compare this with the best n-term approximation with respect to an optimal Riesz basis. We consider worst case errors, where f is an element of the unit ball of a Hilbert space. We apply our results to boundary value problems for elliptic PDEs that are given by an isomorphism A :...

Towards Polyalgorithmic Linear System Solvers for Nonlinear Elliptic Problems

We investigate the performance of several preconditioned Conjugate-Gradient-like algorithms and a standard stationary iterative method (block-line-SOR) on linear systems of equations as they arise from a nonlinear elliptic ame sheet problem simulation. The nonlinearity forces a pseudo-transient continuation process that makes the problem parabolic and thus compacts the spectrum of the Jacobian ...

Nonlinear Elliptic Problems

with Aa having at most polynomial growth, by applying a general theorem concerning nonlinear functional equations in reflexive Banach spaces. Our result in [ l] extended and generalized results announced earlier by M. I. Visik [6; 7; 8] and obtained by more concrete analytic arguments. Visik's detailed account of his results which has just appeared in [9] has one feature which goes beyond the f...