177,968 research outputs found
Schrödinger–Newton equations in dimension two via a Pohozaev–Trudinger log-weighted inequality
No full textWe study the following Choquard type equation in the whole plane (C)-Δu+V(x)u=(I2∗F(x,u))f(x,u),x∈R2where I2 is the Newton logarithmic kernel, V is a bounded Schrödinger potential and the nonlinearity f(x, u), whose primitive in u vanishing at zero is F(x, u), exhibits the highest possible growth which is of exponential type. The competition between the logarithmic kernel and the exponential nonlinearity demands for new tools. A proper function space setting is provided by a new weighted version of the Pohozaev–Trudinger inequality which enables us to prove the existence of variational, in particular finite energy solutions to (C)
Adams' inequality and limiting Sobolev embeddings into Zygmund spaces
No full textWe exhibit sharp embedding constants for Sobolev spaces of any order into
Zygmund spaces, obtained as the product of sharp embedding constants for second
order Sobolev space into Lorentz spaces. As a consequence, we derive a new proof
of Adams’ inequality, which holds in the larger hypotheses of homogenoeous Navier
boundary contidions
Premessa
No full textLa Premessa illustra i contenuti del numero monografico di "Testo" intitolato "La provincia nella letteratura italiana dell'Ottocento e del Novecento", a cura di Stefania Baragetti e Maria Chiara Tarsi
Uniqueness of positive solutions of nonlinear elliptic equations with exponential growth
No full textBy combining a technique inspired to the theory of sublinear elliptic equations with the Emden-Fowler inversion technique of Atkinson and Peletier, we obtain uniqueness of positive solutions of the following equation -Δu = λueu θ in B, u > 0, u = 0 on ∂B, where B ⊂ Rn is the ball of radius one, λ > 0 and 1 < ν ≤ 2
On the existence and radial symmetry of maximizers for functionals with critical exponential growth in R^2
No full textExistence of solitary waves for supercritical Schroedinger systems in dimension two
No full textWe prove existence of variational solutions for the Hamiltonian coupling of nonlinear Schrödinger equations in the whole plane, when the nonlinearities exhibit supercritical growth with respect to the Trudinger–Moser inequality. We discover linking type solutions which have finite energy in a suitable Lorentz–Sobolev space settin
Perturbation of symmetry and multiplicity of solutions for strongly indefinite elliptic systems
No full textWe consider the following elliptic system:
-\Delta u= |v|^{p-1} v + h(x) %
& x\in \Omega \\
-\Delta v= |u|^{q-1} u + k(x) %
& x\in \Omega \\
u=v=0 & x\in \partial \Omega
where \Omega \subset R^N, N\geq 3 is a smooth bounded domain. If h(x)= k(x)= 0 the system presents a natural Z_2 symmetry, which guarantees the existence of infinitely many solutions. In this paper we show that the multiplicity structure can be maintained if (p,q)lies below a suitable curve in R^2
Perturbation from symmetry and multiplicity of solutions for elliptic problems with subcritical exponential growth in R^2
No full textWe consider the following boundary value problem {-Δu = g(x, u) + f(x, u) x ∈ Ω u = 0 x ∈ ∂Ω where g(x, -ξ) = -g(x,ξ) and g has subcritical exponential growth in R2. Using the method developed by Bolle, we prove that this problem has infinitely many solutions under suitable conditions on the growth of g(u) and f(u)
On Trudinger–Moser type inequalities involving Sobolev–Lorentz spaces
No full textGeneralizations of the Trudinger-Moser inequality to Sobolev-Lorentz spaces with weights are considered. The weights in these
spaces allow for the addition of certain lower order terms in the exponential integral. We prove an explicit relation between
the weights and the lower order terms; furthermore, we show that the resulting inequalities are sharp, and that there are
related phenomena of concentration-compactness
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