1,721,002 research outputs found
Positive solutions of nonlinear Schrödinger–Poisson systems with radial potentials vanishing at infinity
Full text linkWe deal with a weighted nonlinear Schrodinger-Poisson system, allowing the potentials to vanish at infinity
Embedding theorems and existence results for nonlinear Schrödinger-Poisson systems with unbounded and vanishing potentials
No full textMotivated by existence results for positive solutions of non-autonomous nonlinear Schrödinger-Poisson systems with potentials possibly unbounded or vanishing at infinity, we prove embedding theorems for weighted Sobolev spaces. We both consider a general framework and spaces of radially symmetric functions when assuming radial symmetry of the potentials. © 2011 Elsevier Inc
New multiplicity results for critical p-Laplacian problems
Full text linkWe prove new multiplicity results for the Brézis-Nirenberg problem for the p-Laplacian. Our proofs are based on a new abstract critical point theorem involving the Z2-cohomological index that requires less compactness than the (PS) condition
Minimal disc-type surfaces embedded in a perturbed cylinder
No full textIn the present note, we deal with small perturbations of an infinite cylinder in three-dimensional Euclidian space. We find minimal disc-type surfaces embedded in the cylinder and intersecting its boundary perpendicularly. The existence and localization of those minimal discs is a consequence of a non-degeneracy condition for the critical points of a functional related to the oscillations of the cylinder from the flat configuration
Foliations of small tubes in Riemannian manifolds by capillary minimal discs
No full textLetting Γ be an embedded curve in a Riemannian manifold M, we prove the existence of minimal disc-type surfaces centered at Γ inside the surface of revolution of M around Γ, having small radius, and intersecting it with constant angles. In particular we obtain that small tubular neighborhoods can be foliated by minimal discs. © 2008 Elsevier Ltd. All rights reserved
Groundstate asymptotics for a class of singularly perturbed p-Laplacian problems in RN
No full textWe study the asymptotic behaviour of positive groundstate solutions to the quasilinear elliptic equation [Figure not available: see fulltext.]where 1 < p< N, p< q< l< + ∞ and ε> 0 is a small parameter. For ε→ 0 , we give a characterization of asymptotic regimes as a function of the parameters q, l and N. In particular, we show that the behaviour of the groundstates is sensitive to whether q is less than, equal to, or greater than the critical Sobolev exponent p∗:=pNN-p
A regularity result for the p-laplacian near uniform ellipticity
Full text linkWe consider weak solutions to a class of Dirichlet boundary value problems involving the p-Laplace operator, and prove that the second weak derivatives are in Lq with q as large as it is desirable, provided p is suffciently close to p0 = 2. We show that this phenomenon is driven by the classical Calderón-Zygmund constant. As a byproduct of our analysis we show that C1,α regularity improves up to C1,1, when p is close enough to 2. This result we believe is particularly interesting in higher dimensions n>2, when optimal C1,α regularity is related to the optimal regularity of p-harmonic mappings, which is still open
On Coron's problem for the p-Laplacian
Full text linkWe prove that the critical problem for the p-Laplacian operator admits a nontrivial solution in annular shaped domains with sufficiently small inner hole. This extends Coron's result [4] to a class of quasilinear problems
Concentration on circles for nonlinear schrödinger-poisson systems with unbounded potentials vanishing at infinity
No full textThe present paper is devoted to weighted nonlinear Schrödinger-Poisson systems with potentials possibly unbounded and vanishing at infinity. Using a purely variational approach, we prove the existence of solutions concentrating on a circle. © 2012 World Scientific Publishing Company
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