1,720,997 research outputs found
On the number of sign-changing solutions of a semiclassical nonlinear Schrödinger equation
No full textMagnetostatic solutions for a semilinear perturbation of the maxwell equations
No full textIn this paper we consider a model introduced in [3] which describes the interaction between the matter and the electromagnetic field from a unitarian standpoint. This model is based on a semilinear perturbation of the Maxwell equations and, in the magnetostatic case, reduces to the following nonlinear elliptic degenerate equation: ∇ × (∇ × A) = W'((A(2)A, where "∇×" is the curl operator, W: R → R is a suitable nonlinear term, and A: R3 → R3 is the gauge potential associated with the magnetic field H. We prove the existence of a nontrivial finite energy solution with a kind of cylindrical symmetry. The proof is carried out by using a suitable variational framework based on the Hodge decomposition, which is crucial in order to handle the strong degeneracy of the equation. Moreover, the use of a natural constraint and a concentrationcompactness argument are also required
Blow-up phenomena for the Liouville equation with a singular source of integer multiplicity
No full textWe are concerned with the existence of blowing-up solutions to the following boundary value problem −Δu=λa(x)eu−4πNδ0 in Ω,u=0 on ∂Ω where Ω is a smooth and bounded domain in R2 such that 0∈Ω a(x) is a positive smooth function, N is a positive integer and λ>0 is a small parameter. Here δ0 defines the Dirac measure with pole at 0. We find conditions on the function a and on the domain Ω under which there exists a solution uλ blowing up at 0 and satisfying λ∫Ωa(x)euλ→8π(N+1) as λ→0+
Semiclassical limit for a quasilinear elliptic field equation: one-peack and multi-peack solutions
No full textPrescribed Gauss curvature problem on singular surfaces
No full textWe study the existence of at least one conformal metric of prescribed Gaussian curvature on a closed surface Σ admitting conical singularities of orders αi ’s at points pi ’s. In particular, we are concerned with the case where the prescribed Gaussian curvature is sign-changing. Such a geometrical problem reduces to solving a singular Liouville equation. By employing a min–max scheme jointly with a finite dimensional reduction method, we deduce new perturbative results providing existence when the quantity χ(Σ)+∑iαi approaches a positive even integer, where χ(Σ) is the Euler characteristic of the surface Σ
Existence, Multiplicity and Profile of Sign-Changing Clustered Solutions of a Semiclassical Nonlinear Schrödinger Equation
No full textWe study the existence and multiplicity of sign-changing solutions for the Dirichlet problem
{-epsilon(2) Delta v + V(x)v = f(v) in Omega,
v = 0 on partial derivative Omega,
where epsilon is a small positive parameter, Omega is a smooth, possibly unbounded, domain, f is a superlinear and subcritical nonlinearity, V is a positive potential bounded away from zero. No symmetry on V or on the domain Omega is assumed. It is known by Kang and Wei (see [X. Kang, J. Wei, On interacting bumps of semiclassical states of nonlinear Schrodinger equations, Adv. Differential Equations 5 (2000) 899-928]) that this problem has positive clustered solutions with peaks approaching a local maximum of V. The aim of this paper is to show the existence of clustered solutions with mixed positive and negative peaks concentrating at a local minimum point, possibly degenerate, of V. (C) 2009 Elsevier Masson SAS. All rights reserved
Prescribed Gauss curvature problem on singular surfaces
Full text linkWe study the existence of at least one conformal metric of prescribed Gaussian curvature on a closed surface Σ admitting conical singularities of orders αi’s at points pi’s. In particular, we are concerned with the case where the prescribed Gaussian curvature is sign-changing. Such a geometrical problem reduces to solving a singular Liouville equation. By employing a min–max scheme jointly with a finite dimensional reduction method, we deduce new perturbative results providing existence when the quantity χ(Σ) + ∑_ i α_i approaches a positive even integer, where χ(Σ) is the Euler characteristic of the surface Σ
Existence of static solutions of the semilinear Maxwell equations
No full textAbstract In this paper we study a model which describes the relation of the matter
and the electromagnetic field from a unitarian standpoint in the spirit of the
ideas of Born and Infeld. This model, introduced in [1], is based on a semilinear
perturbation of the Maxwell equation (SME). The particles are described by the
finite energy solitary waves of SME whose existence is due to the presence of
the nonlinearity. In the magnetostatic case (i.e. when the electric field E = 0 and
the magnetic field H does not depend on time) the semilinear Maxwell equations
reduce to the following semilinear equation
∇×(∇×A) = f
(A) (1)
where “∇×” is the curl operator, f is the gradient of a smooth function f :R3→R
and A : R3 → R3 is the gauge potential related to the magnetic field H (H =
∇×A). The presence of the curl operator causes (1) to be a strongly degenerateelliptic equation. The existence of a nontrivial finite energy solution of (1) having
a kind of cylindrical symmetry is proved. The proof is carried out by using a
variational approach based on two main ingredients: the Principle of symmetric
criticality of Palais, which allows to avoid the difficulties due to the curl operator,
and the concentration-compactness argument combined with a suitable minimization
argument
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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