1,720,991 research outputs found
Solutions with many mixed positive and negative interior spikes for a semilinear Neumann problem
No full textWe study the existence of sign-changing multiple interior spike solutions for the following Neumann problem ε^2∆v−v+f(v)=0inΩ, ∂v =0 on ∂Ω, where Ω is a smooth bounded domain of R^N , ε is a small positive parameter, f is a superlinear, subcritical and odd nonlinearity. No symmetry on Ω is assumed. To our knowledge, only positive interior peak solutions have been obtained for this problem and it remains a question whether or not multiple interior peak solutions with mixed positive and negative peaks exist. In this paper we assume that Ω is a two-dimensional strictly convex domain and, provided that k is sufficiently large, we construct a (k + 1)-peak solutions with k positive interior peaks aligned on a closed curve near ∂Ω and 1 negative interior peak located in a more centered part of Ω
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
Multi-bubble solutions for a slightly supercritical elliptic problem in a domain with a small hole
No full textWe are concerned with the existence and the asymptotic analysis when the parameter εtends to 0of solutions with multiple concentration for the following almost critical problem:
−Δu = u^{(N+2)/(N−2)}+ε in Ω, u>0 inΩ, u= 0 on ∂Ω,
where Ωis a bounded domain in RNwith a smooth boundary and N≥3. Weare interested in concentration phenomena from the supercritical side ε →0+. In particular we prove that, if Ωhas a small and not necessarily symmetric hole, then for any fixed odd integer k≥3 there exists a family of solutions which develops a multiple bubble-shape as ε →0+, blowing up at kdifferent points in Ω. This extends the previous result by Del Pino, Felmer and Musso [13], where solutions with a two-bubbleprofile are constructed
Semiclassical states for the nonlinear Schrödinger equation with the electromagnetic field
No full textVariations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Sign-changing blow-up solutions for Hénon type elliptic equations with exponential nonlinearity
No full textWe study the existence of sign-changing solutions with multiple concentration to the following boundary value problem
−Δu=ε^2|x|^{2α}(e^u−e{−u}) in Ω,u=0 on ∂Ω,
where α>0, Ω is a smooth bounded domain in R2 containing the origin, ε>0 is a small parameter. In particular we prove that if α≠1 then a nodal solution exists with a number of mixed positive and negative blow-up points up to 4
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