1,721,154 research outputs found

    Ground state solutions fora nonlinear Choquard equation

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    We discuss the existence of ground state solutions for the Choquard equation-Δu + u-(Iα←F(u)) F'(u) inRN. We prove the existence of solutions under general hypotheses, investigating in particular the case of a homogeneous nonlinearity F(u) =|u|p/p. The cases N = 2 and N ≥ 3 are treated differently in some steps. The solutions are found through a variational mountain-pass strategy. The results presented are contained in the papers [8, 2]

    A Moser-Trudinger inequality for the singular Toda system

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    In this paper we prove a sharp version of the Moser-Trudinger inequality for the Euler-Lagrange functional of a singular Toda system, motivated by the study of models in Chern-Simons theory. Our result extends those in [14] and [37] for the scalar case, as well as that in [23] for the regular Toda system. We expect this inequality to be a basic tool to attack variationally the existence problem under general assumption

    A unified approach of blow-up phenomena for two-dimensional singular Liouville systems

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    We consider generic 2 × 2 singular Liouville systems [Equation presented here] where Ω∈ 0 is a smooth bounded domain in R2 possibly having some symmetry with respect to the origin, δ0 is the Dirac mass at 0, λ1, λ2 are small positive parameters and a, b, α1, α2 > 0. We construct a family of solutions to (∗) which blow up at the origin as λ1 → 0 and λ2 → 0 and whose local mass at the origin is a given quantity depending on a, b, α1, α2. In particular, if ab < 4 we get finitely many possible blow-up values of the local mass, whereas if ab ≥ 4 we get infinitely many. The blow-up values are produced using an explicit formula which involves Chebyshev polynomials

    A note on compactness properties of the singular Toda system

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    In this note, we consider blow-up for solutions of the SU(3) Toda system on a compact surface σ. In particular, we give a complete proof of the compactness result stated by Jost, Lin and Wang in [11] and we extend it to the case of singularities. This is a necessary tool to find solutions through variational methods

    Renewable energy industries in Europe. Are they successful in the Chinese market?

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    This article analyses the number, type and presence of European companies – Italian, Spanish, French, German, Dutch, Rumanian, Bulgarian and English – operating in the renewable energies industry in international markets. Enterprises supplying energy from various sources and at different points of the supply chain have long faced the challenges that international and geographically distant markets such as China pose. Specifically, European enterprises appear to encounter difficulties in approaching the Chinese market, which is rapidly developing as a result of the latest five-year plan setting energy and climate change targets and policies. Indeed, the number of European firms investing in China is low due to their small size, high cultural distance and inadequate management strategies. Through the analysis of two business cases (Asja and Caleffi) that have established partnerships and a WFOE in China, the article identifies the main elements of their management strategies that led to successfully operating in China

    The Renewable Energy Industry in Europe: Business and Internationalization Models for China

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    This article analyses the number, type and presence of European companies Italian, Spanish, French, German, Dutch, Rumanian, Bulgarian English operating in the renewable energies industry in international markets, with a focus on China

    A double mean field equation related to a curvature prescription problem

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    We study a double mean field–type PDE related to a prescribed curvature problem on compacts surfaces with boundary: {−Δu=2ρ([Formula presented]−[Formula presented]) [Formula presented] in are real parameters, K,h are smooth positive functions on Σ and ∂Σ respectively and ν is the outward unit normal vector to ∂Σ. We provide a general blow–up analysis, then a Moser–Trudinger inequality, which gives energy–minimizing solutions for some range of parameters. Finally, we provide existence of min–max solutions for a wider range of parameters, which is dense in the plane if Σ is not simply connected
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