Angela Pistoia

Bio: Angela Pistoia is an academic researcher from Sapienza University of Rome. The author has contributed to research in topics: Riemannian manifold & Bounded function. The author has an hindex of 29, co-authored 213 publications receiving 3130 citations. Previous affiliations of Angela Pistoia include University of Pisa.

On the existence of blowing-up solutions for a mean field equation ✩

Abstract: In this paper we construct single and multiple blowing-up solutions to the mean field equation: {−Δu=λV(x)eu∫ΩV(x)euin Ω,u=0on ∂Ω, where Ω is a smooth bounded domain in R2, V is a smooth function positive somewhere in Ω and λ is a positive parameter.

Existence of multipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory

Abstract: We study a perturbed semilinear problem with Neumann boundary condition \[ \cases{ -\varepsilon^2\Delta u+u=u^p & {\rm in} \Omega \cr &\cr u>0 & {\rm in} \Omega\cr &\cr {{\partial u}\over{\partial u}}=0& {\rm in} \partial\Omega,\cr} \] where $\Omega$ is a bounded smooth domain of ${mathbb{R}}^N$ , $N\ge2$ , $\varepsilon>0$ , $1 < p < {{N+2}\over{N-2}}$ if $N\ge3$ or $p>1$ if $N=2$ and $ u$ is the unit outward normal at the boundary of $\Omega$ . We show that for any fixed positive integer K any “suitable” critical point $(x_0^1,\dots,x_0^K)$ of the function \begin{eqnarray*} \lefteqn{\varphi_K(x^1,\dots,x^K)} &=& \min\left\{{\rm dist}(x^i,{\partial\Omega}),{|x^j-x^l|\over2} \mid i,j,l=1.\dots,K, j e l\right\} \end{eqnarray*} generates a family of multiple interior spike solutions, whose local maximum points $x_\varepsilon^1,\dots,x_\varepsilon^K$ tend to $x_0^1,\dots,x_0^K$ as $\varepsilon$ tends to zero.

ultispike solutions for a nonlinearelliptic problem involving critical Sobolev exponent

Abstract: The main purpose of this paper is to construct families of positive solutions for the equation formula math. which blow-up and concentrate in k ≥ 1 different points of Q as e goes to 0. We exhibit some examples of contractible domains where a large number of solutions exists.

An Introduction to the Study of Stellar Structure

Abstract: EDDINGTON'S “Internal Constitution of the Stars” was published in 1926 and gives what now ranks as a classical account of his own researches and of the general state of the theory at that time. Since then, a tremendous amount of work has appeared. Much of it has to do with the construction of stellar models with different equations of state applying in different zones. Other parts deal with the effects of varying chemical composition, with pulsation and tidal and rotational distortion of stars, and with the precise relations between the interior and the atmosphere of a star. The striking feature of all this work is that so much can be done without assuming any particular mechanism of stellar energy-generation. Only such very comprehensive assumptions are made about the distribution and behaviour of the energy sources that we may expect future knowledge of their mechanism to lead mainly to more detailed results within the framework of the existing general theory. An Introduction to the Study of Stellar Structure By S. Chandrasekhar. (Astrophysical Monographs sponsored by The Astrophysical Journal.) Pp. ix+509. (Chicago: University of Chicago Press; London: Cambridge University Press, 1939.) 50s. net.

Superlinear Parabolic Problems: Blow-up, Global Existence and Steady States

Abstract: Preliminaries.- Model Elliptic Problems.- Model Parabolic Problems.- Systems.- Equations with Gradient Terms.- Nonlocal Problems.

Nonlinear partial differential equations with applications

Abstract: Preface.- Preface to the 2nd edition.- Notational conventions.- 1 Preliminary general material.- I Steady-state problems.- 2 Pseudomonotone or weakly continuous mappings.- 3 Accretive mappings.- 4 Potential problems: smooth case.- 5 Nonsmooth problems variational inequalities.- 6. Systems of equations: particular examples.- II Evolution problems.- 7 Special auxiliary tools.- 8 Evolution by pseudomonotone or weakly continuous mappings.- 9 Evolution governed by accretive mappings.- 10 Evolution governed by certain set-valued mappings.- 11 Doubly-nonlinear problems.- 12 Systems of equations: particular examples.- References.- Index.

Singular limits in liouville-type equations

Abstract: We consider the boundary value problem $ \Delta u + \varepsilon ^{2} k{\left( x \right)}e^{u} = 0$ in a bounded, smooth domain $\Omega$ in $ \mathbb{R}^{{\text{2}}} $ with homogeneous Dirichlet boundary conditions. Here $$ \varepsilon > 0,k(x) $$ is a non-negative, not identically zero function. We find conditions under which there exists a solution $ u_{\varepsilon } $ which blows up at exactly m points as $ \varepsilon \to 0 $ and satisfies $ \varepsilon ^{2} {\int_\Omega {ke^{{u_{\varepsilon } }} \to 8m\pi } }% $ . In particular, we find that if $k\in C^2(\bar\Omega)$ , $ \inf _{\Omega } k > 0 $ and $\Omega$ is not simply connected then such a solution exists for any given $m \ge 1$

Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part I

Abstract: We deal with the existence of positive radial solutions concentrating on spheres to a class of singularly perturbed elliptic problems like −ɛ2Δu+V(|x|)u=u p ,uH 1 (ℝ n ). Under suitable assumptions on the auxiliary potential M(r)=r n−1 V θ (r), θ(p+1)/(p−1)−1/2, we provide necessary and sufficient conditions for concentration as well as the bifurcation of non-radial solutions.