The search session has expired. Please query the service again.

All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 26 Next

Displaying 501 – 520 of 601

Showing per page

Spectrum of the weighted Laplace operator in unbounded domains

Alexey Filinovskiy (2011)

Mathematica Bohemica

We investigate the spectral properties of the differential operator - r s Δ , s ≥ 0 with the Dirichlet boundary condition in unbounded domains whose boundaries satisfy some geometrical condition. Considering this operator as a self-adjoint operator in the space with the norm ∥ u ∥ L 2 , s ( Ω ) 2 = ∫ Ω r - s | u | 2 d x , we study the structure of the spectrum with respect to the parameter s . Further we give an estimate of the rate of condensation of discrete spectra when it changes to continuous.

Stability of solutions for an abstract Dirichlet problem

Marek Galewski (2004)

Annales Polonici Mathematici

We consider continuous dependence of solutions on the right hand side for a semilinear operator equation Lx = ∇G(x), where L: D(L) ⊂ Y → Y (Y a Hilbert space) is self-adjoint and positive definite and G:Y → Y is a convex functional with superquadratic growth. As applications we derive some stability results and dependence on a functional parameter for a fourth order Dirichlet problem. Applications to P.D.E. are also given.

Stability results for some nonlinear elliptic equations involving the p-Laplacian with critical Sobolev growth

Bruno Nazaret (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This article is devoted to the study of a perturbation with a viscosity term in an elliptic equation involving the p-Laplacian operator and related to the best contant problem in Sobolev inequalities in the critical case. We prove first that this problem, together with the equation, is stable under this perturbation, assuming some conditions on the datas. In the next section, we show that the zero solution is strongly isolated in some sense, among the space of the solutions. Actually, we end the...

Stationary solutions of the generalized Smoluchowski-Poisson equation

Robert Stańczy (2008)

Banach Center Publications

The existence of steady states in the microcanonical case for a system describing the interaction of gravitationally attracting particles with a self-similar pressure term is proved. The system generalizes the Smoluchowski-Poisson equation. The presented theory covers the case of the model with diffusion that obeys the Fermi-Dirac statistic.

Stationary states for a two-dimensional singular Schrödinger equation

Paolo Caldiroli, Roberta Musina (2001)

Bollettino dell'Unione Matematica Italiana

In questo articolo studiamo problemi di Dirichlet singolari, lineari e semilineari, della forma x 2 ⁢ Δ ⁢ u = f ⁢ u in Ω , u = 0 su ∂ ⁡ Ω , dove Ω è un dominio in R 2 e f ⁢ u = λ ⁢ u o f ⁢ u = λ ⁢ u + u p - 2 ⁢ u con p > 2 (o nonlinearità più generali). In tali problemi bidimensionali emergono alcune difficoltà a causa della non validità della disuguaglianza di Hardy in R 2 e a causa delle invarianze dell'equazione - x 2 ⁢ Δ ⁢ u = f ⁢ u . Pertanto opportune condizioni su λ e Ω sono necessarie al fine di garantire l'esistenza di una soluzione positiva. Per esempio, se Γ 0 è una curva non costante...

Structure of stable solutions of a one-dimensional variational problem

Nung Kwan Yip (2006)

ESAIM: Control, Optimisation and Calculus of Variations

We prove the periodicity of all H2-local minimizers with low energy for a one-dimensional higher order variational problem. The results extend and complement an earlier work of Stefan Müller which concerns the structure of global minimizer. The energy functional studied in this work is motivated by the investigation of coherent solid phase transformations and the competition between the effects from regularization and formation of small scale structures. With a special choice of a bilinear double...

Currently displaying 501 – 520 of 601