Browsing by Author "Musso, Monica"
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- ItemBoundary singularities for weak solutions of semilinear elliptic problems(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2007) del Pino, Manuel; Musso, Monica; Pacard, FrankLet Omega be a bounded domain in R-N, N >= 2, with smooth boundary partial derivative Omega. We construct positive weak solutions of the problem Delta u + u(p) = 0 in Omega, which vanish in a suitable trace sense on partial derivative Omega, but which are singular at prescribed isolated points if p is equal or slightly above N+1/N-1. Similar constructions are carried out for solutions which are singular at any given embedded submanifold of partial derivative Omega of dimension k epsilon [0, N -2], if p equals or it is slightly above N-k-1/N-k-1, and even on countable families of these objects, dense on a given closed set. The role of the exponent N+1/N-1 (first discovered by Brezis and Turner [H. Brezis, R. Turner, N-1 On a class of superlinear elliptic problems, Comm. Partial Differential Equations 2 (1977) 601-614]) for boundary regularity, parallels that of N/N-2 for interior singularities. (c) 2007 Elsevier Inc. All rights reserved.
- ItemConcentrating solutions for a planar elliptic problem involving nonlinearities with large exponent(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2006) Esposito, Pierpaolo; Musso, Monica; Pistoia, AngelaWe consider the boundary value problem Delta u + u(P) = 0 in a bounded, smooth domain Omega in R-2 with homogeneous Dirichlet boundary condition and p a large exponent. We find topological conditions on Omega which ensure the existence of a positive solution up concentrating at exactly m points as p -> infinity. In particular, for a nonsimply connected domain such a solution exists for any given m >= 1. (c) 2006 Elsevier Inc. All rights reserved.
- ItemLarge energy entire solutions for the Yamabe equation(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2011) del Pino, Manuel; Musso, Monica; Pacard, Frank; Pistoia, AngelaWe consider the Yamabe equation Delta u + n(n-2_/4 vertical bar u vertical bar 4/n-2 u = 0 in R(n), n >= 3. Let k >= 1 and xi(k)(j) = (e(2j pi u/k), 0) is an element of R(n) = C x R(n-2). For all large k we find a solution of the form u(k)(x)= u(x) - Sigma(k)(j=1) mu(k) (-n-2/2) U X (mu(-1)(k) (x - xi(j)) +o(1), where U(x) = (2/1+vertical bar x vertical bar(2)) (n-2/2), mu(k) = c(n)/k(2) for n >= 4, mu k = c/k(2)(logk)(2) for n =3 and o(1) -> 0 uniformly as k -> +infinity. (C) 2011 Elsevier Inc. All rights reserved.
- ItemMorse index and bifurcation of p-geodesics on semi Riemannian manifolds(EDP SCIENCES S A, 2007) Musso, Monica; Pejsachowicz, Jacobo; Portaluri, AlessandroGiven a one-parameter family {g(lambda) :lambda is an element of [ a, b]} of semi Riemannian metrics on an n-dimensional manifold M, a family of time-dependent potentials {V-lambda: lambda is an element of [a, b]} and a family {sigma(lambda): lambda is an element of [ a, b]} of trajectories connecting two points of the mechanical system defined by ( g(lambda),V-lambda), we show that there are trajectories bifurcating from the trivial branch s. if the generalized Morse indices mu(sigma(a)) and mu(sigma(a)) are different. If the data are analytic we obtain estimates for the number of bifurcation points on the branch and, in particular, for the number of strictly conjugate points along a trajectory using an explicit computation of the Morse index in the case of locally symmetric spaces and a comparison principle of Morse Schrodenberg type.
- ItemMultipeak solutions to the Bahri-Coron problem in domains with a shrinking hole(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2009) Clapp, Monica; Musso, Monica; Pistoia, AngelaWe construct positive and sign changing multipeak solutions to the Pure critical exponent problem in a bounded domain with a shrinking hole, having a peak which concentrates at some point inside the shrinking hole (i.e. outside the domain) and one or more peaks which concentrate at interior points of the domain. These are, to Our knowledge, the first multipeak solutions in a domain with a single small hole. (C) 2008 Elsevier Inc. All rights reserved.
- ItemNew solutions for Trudinger-Moser critical equations in R-2(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2010) del Pino, Manuel; Musso, Monica; Ruf, BernhardLet Omega be a bounded, smooth domain in R-2. We consider critical points of the Trudinger-Moser type functional J(lambda) (u) = 1/2 integral(Omega)vertical bar del u vertical bar(2) - lambda/2 integral(Omega)e(u2) in H-0(1)(Omega), namely solutions of the boundary value problem Delta u + lambda ue(u2) = 0 with homogeneous Dirichlet boundary conditions, where lambda > 0 is a small parameter. Given k >= 1 we find conditions under which there exists a solution u(lambda) which blows up at exactly k points in Omega as lambda -> 0 and J(lambda)(u(lambda)) -> 2k pi. We find that at least one such solution always exists if k = 2 and Omega is not simply connected. If Omega has d >= 1 holes, in addition d + 1 bubbling solutions with k = 1 exist. These results are existence counterparts of one by Druet in [O. Druet, Multibump analysis in dimension 2: Quantification of blow-up levels, Duke Math. J. 132 (2) (2006) 217-269] which classifies asymptotic bounded energy levels of blow-up solutions for a class of nonlinearities of critical exponential growth, including this one as a prototype case. (C) 2009 Elsevier Inc. All rights reserved.
- ItemNONDEGENERACY OF ENTIRE SOLUTIONS OF A SINGULAR LIOUVILLLE EQUATION(AMER MATHEMATICAL SOC, 2012) del Pino, Manuel; Esposito, Pierpaolo; Musso, MonicaWe establish nondegeneracy of the explicit family of finite mass solutions of the Liouvillle equation with a singular source of integer multiplicity, in the sense that all bounded elements in the kernel of the linearization correspond to variations along the parameters of the family.
- ItemNonradial Solutions to Critical Elliptic Equations of Caffarelli-Kohn-Nirenberg Type(OXFORD UNIV PRESS, 2012) Musso, Monica; Wei, JunchengWe build an unbounded sequence of nonradial solutions for
- ItemOn spikes concentrating on line-segments to a semilinear Neumann problem(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2011) Ao, Weiwei; Musso, Monica; Wei, JunchengWe consider the following singularly perturbed Neumann problem
- ItemOn the existence and profile of nodal solutions for a two-dimensional elliptic problem with large exponent in nonlinearity(WILEY, 2007) Esposito, Pierpaolo; Musso, Monica; Pistoia, AngelaWe study the existence of nodal solutions to the boundary value problem -Delta u = \u\(p-1)u in a bounded, smooth domain Omega in R-2, with homogeneous Dirichlet boundary condition, when p is a large exponent. We prove that, for p large enough, there exist at least two pairs of solutions which change sign exactly once and whose nodal lines intersect the boundary of Omega.
- ItemSign changing solutions to a Bahri-Coron's problem in pierced domains(AMER INST MATHEMATICAL SCIENCES-AIMS, 2008) Musso, Monica; Pistoia, AngelaWe consider the problem
- ItemSign changing solutions to a nonlinear elliptic problem involving the critical Sobolev exponent in pierced domains(GAUTHIER-VILLARS/EDITIONS ELSEVIER, 2006) Musso, Monica; Pistoia, AngelaWe consider the problem Delta u + \u\(4/n-2) u = 0 in Omega(epsilon), u = 0 on partial derivative Omega(epsilon), where Omega(epsilon) := Omega \ B (0, epsilon) and Omega is a bounded smooth domain in R(N), which contains the origin and is symmetric with respect to the origin, N >= 3 and epsilon is a positive parameter. As epsilon goes to zero, we construct sign changing solutions with multiple blow up at the origin. (C) 2006 Elsevier Masson SAS. All rights reserved.
- ItemSign Changing Tower of Bubbles for an Elliptic Problem at the Critical Exponent in Pierced Non-Symmetric Domains(TAYLOR & FRANCIS INC, 2010) Ge, Yuxin; Musso, Monica; Pistoia, AngelaWe consider the problem [image omitted] in epsilon, u=0 on epsilon, where epsilon: =\{B(a, epsilon) B(b, epsilon)}, with a bounded smooth domain in N, N epsilon 3, ab two points in , and epsilon is a positive small parameter. As epsilon goes to zero, we construct sign changing solutions with multiple blow up both at a and at b.
- ItemSingular limits for the bi-Laplacian operator with exponential nonlinearity in R-4(GAUTHIER-VILLARS/EDITIONS ELSEVIER, 2008) Clapp, Monica; Munoz, Claudio; Musso, MonicaLet Omega be a bounded smooth domain in R-4 such that for some integer d >= 1 its d-th singular cohomology group with coefficients in some field is not zero, then problem
- ItemStanding waves for supercritical nonlinear Schrodinger equations(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2007) Davila, Juan; del Pino, Manuel; Musso, Monica; Wei, JunchengLet V (x) be a non-negative, bounded potential in R-N, N >= 3 and p supercritical, p > N+2/N-2. We look for positive solutions of the standing-wave nonlinear Schrodinger equation Delta u - V(x)u + u(P) = 0 in R-N, with u(x) -> 0 as vertical bar x vertical bar -> +infinity. We prove that if V(x) = 0(vertical bar x vertical bar(-2)) as vertical bar x vertical bar -> +infinity, then for N >= 4 and p > N+1/N-3 this problem admits a continuum of solutions. If in addition we have, for instance, V (x) = 0 (vertical bar x vertical bar-mu) with mu > N, then this result still holds provided that N >= 3 and p > N+2/N-2. Other conditions for solvability, involving behavior of V at infinity, are also provided. (C) 2007 Elsevier Inc. All rights reserved.
- ItemStationary solutions to a Keller-Segel chemotaxis system(IOS PRESS, 2006) Musso, Monica; Wei, JunchengWe consider the following stationary Keller-Segel system from chemotaxis
- ItemTRIPLE JUNCTION SOLUTIONS FOR A SINGULARLY PERTURBED NEUMANN PROBLEM(SIAM PUBLICATIONS, 2011) Ao, Weiwei; Musso, Monica; Wei, JunchengWe consider the singularly perturbed Neumann problem epsilon(2)Delta u - u + up = 0, u > 0 in Omega, partial derivative u/partial derivative v = 0 on partial derivative Omega, where p > 1 and Omega is a smooth and bounded domain in R-2. We construct a class of solutions which consist of large number of spikes concentrated on three line segments with a common endpoint which intersect partial derivative Omega orthogonally.
- ItemTWO-DIMENSIONAL EULER FLOWS WITH CONCENTRATED VORTICITIES(AMER MATHEMATICAL SOC, 2010) del Pino, Manuel; Esposito, Pierpaolo; Musso, MonicaFor a planar model of Euler flows proposed by Tur and Yanovsky (2004), we construct a family of velocity fields w(e) for it fluid in a bounded region Omega, with concentrated vorticities w(e) for epsilon > 0 small. More precisely, given a positive integer a and a sufficiently small complex number a, we find a family of stream functions psi(epsilon) which solve the Liouville equation with Dirac mass source,