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We consider the following Dirichlet problem(formula persented) and f non-negative and non-decreasing. We show existence and uniqueness of solutions uλ for any λ and discuss their asymptotic behavior as λ → −∞. In the expansion of uλ large solutions naturally appear.

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].

Research in neurooncology traditionally requires appropriate in vivo animal models, on which therapeutic strategies are tested before human trials are designed and proceed. Several reproducible animal experimental models, in which human physiologic conditions can be mimicked, are available for studying glioblastoma multiforme. In an ideal rat model, the tumor is of glial origin, grows in predictable and reproducible patterns, closely resembles human gliomas histopathologically, and is weakly or nonimmunogenic. In the current study, we used MRI and histopathologic evaluation to compare the most widely used allogeneic rat glioma model, C6-Wistar, with the F98-Fischer syngeneic rat glioma model in terms of percentage tumor growth or regression and growth rate. In vivo MRI demonstrated considerable variation in tumor volume and frequency between the 2 rat models despite the same stereotactic implantation technique. Faster and more reproducible glioma growth occurred in the immunoresponsive environment of the F98-Fischer model, because the immune response is minimized toward syngeneic cells. The marked inability of the C6-Wistar allogeneic system to generate a reproducible model and the episodes of spontaneous tumor regression with this system may have been due to the increased humoral and cellular immune responses after tumor implantation.

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 assumptions

In this work, a hierarchical variant of a boundary element method and its use in Stokes flow around three-dimensional rigid bodies in steady regime is presented. The proposal is based on the descending hierarchical low-order and self-adaptive algorithm of Barnes-Hut, and it is used in conjunction with an indirect boundary integral formulation of second class, whose source term is a function of the undisturbed velocity. The solution field is the double layer surface density, which is modified in order to complete the eigenvalue spectrum of the integral operator. In this way, the rigid modes are eliminated and both a non-zero force and a non-null torque on the body could be calculated. The elements are low order flat triangles, and an iterative solution by generalized minimal residual (GMRES) is used. Numerical examples include cases with analytical solutions, bodies with edges and vertices, or with intricate shapes. The main advantage of the presented technique is the possibility of considering a greater number of degrees of freedom regarding traditional collocation methods, due to the decreased demand of main memory and the reduction in the computation times.

The aim of this paper is to describe how Italian companies approach the Chinese market and in particular, how they have changed their business model to face the Chinese challenge. Particular emphasis will be given to relationships and their importance to achieve a long-term competitive advantage on that market. The results of a both quantitative and qualitative research are presented. An evolutionary model on sustainable internationalization is then proposed.

The globalization of markets and the emergence of countries characterized by high context and cultural distance, such as China, force companies, regardless of their size, to adapt the entire company, not just its offer. The paper focuses on Italian enterprises and aims to describe how they have changed their business model to face the Chinese challenge. Collaborations and cooperation between actors in the value chain will be the focus of the analysis. The results are based on a qualitative research that investigates a sample of 31 Italian firms operating in different industrial sectors. The paper provides managerial implications based on an evolutionary model proposed for the reading of the conduct of business in international markets.