1,721,541 research outputs found
Alcuni problemi variazionali per equazioni di campo accoppiate con le equazioni di Maxwell
No full textSi presentano i risultati ottenuti nella tesi di Dottorat
Magnetostatic solutions for a semilinear perturbation of the Maxwell equations
No full textIn this paper we consider a model introduced in [3] which describes the interaction between the matter and the electromagnetic field from a unitarian standpoint. This model is based on a semilinear perturbation of the Maxwell equations and, in the magnetostatic case, reduces to the following nonlinear elliptic degenerate equation:
∇×(∇×A)=W′(|A|^2)A,
where "∇×" is the curl operator, W:R→R is a suitable nonlinear term, and A:R^3→R^3 is the gauge potential associated with the magnetic field H. We prove the existence of a nontrivial finite energy solution with a kind of cylindrical symmetry. The proof is carried out by using a suitable variational framework based on the Hodge decomposition, which is crucial in order to handle the strong degeneracy of the equation. Moreover, the use of a natural constraint and a concentration-compactness argument are also required
On the structure of the Nehari set associated to a Schrödinger-Poisson system with prescribed mass: old and new results
No full textIn this paper we apply the fibering method of Pohozaev and the notion of extremal values introduced by Il’yasov to a Schrödinger—Poisson system, with prescribed L2 norm of the unknown, in the whole R3. The method makes clear the role played by the special exponents p = 3, p = 8/3, p = 10/3. In addition to showing that old results can be obtained in a unified way, we exhibit also new ones
An updated review on the role of prescribed exercise in the management of Amyotrophic lateral sclerosis
No full textIntroduction: Amyotrophic Lateral Sclerosis is a group of sporadic or familial disorders, characterized by upper and lower motor neuron involvement, with variable progression. Areas covered: The authors present the role of exercise in counteracting muscle disuse, particularly on limb weakness, that might antagonize denervation. The persistence of inactivity can affect many systems and the patient can develop deconditioning, muscle joint tightness, which causes contractures and pain. The main area of the review is the evaluation of the studies done on ALS exercise rehabilitation protocols, this was done by the evaluation of outcome function and patient independence exerting a positive psychological impact on both patients and caregivers. A second target is underlying differences between endurance and resistance exercise protocols, which may throw light on the biological mechanism of skeletal muscle repair, functional performance, and metabolism. The authors present not only exercise trials but also molecular biomarkers that might help define changes induced by physical rehabilitation. Our findings might help to achieve the best rehabilitation program. A standardized rehabilitation protocol is important: the instructed patients may continue therapy at home or be followed by telemedicine. Expert opinion: This review evaluates exercise rehabilitation, a controversial issue, evidence is weak and non-conclusive but represents the art status
Magnetostatic solutions for a semilinear perturbation of the maxwell equations
No full textIn this paper we consider a model introduced in [3] which describes the interaction between the matter and the electromagnetic field from a unitarian standpoint. This model is based on a semilinear perturbation of the Maxwell equations and, in the magnetostatic case, reduces to the following nonlinear elliptic degenerate equation: ∇ × (∇ × A) = W'((A(2)A, where "∇×" is the curl operator, W: R → R is a suitable nonlinear term, and A: R3 → R3 is the gauge potential associated with the magnetic field H. We prove the existence of a nontrivial finite energy solution with a kind of cylindrical symmetry. The proof is carried out by using a suitable variational framework based on the Hodge decomposition, which is crucial in order to handle the strong degeneracy of the equation. Moreover, the use of a natural constraint and a concentrationcompactness argument are also required
A perturbation approach for the Schrödinger-Born-Infeld system: Solutions in the subcritical and critical case
No full textIn this paper, we study the following Schrödinger-Born-Infeld system with a general nonlinearity {−Δu+u+φu=f(u)+μ|u|4uinR3,−div([Formula presented])=u2inR3,u(x)→0,φ(x)→0,asx→∞, where μ≥0 and f∈C(R,R) satisfies suitable assumptions. This system arises from a suitable coupling of the nonlinear Schrödinger equation and the Born-Infeld theory. We use a new perturbation approach to prove the existence and multiplicity of nontrivial solutions of the above system in the subcritical and critical case. We emphasise that our results cover the case f(u)=|u|p−1u for p∈(2,5/2] and μ=0 which was left in [2] as an open problem
A note on the Schrödinger-Poisson-Slater equation on bounded domains
No full textIn this note we consider the problem (Formula Presented) where u, φ 6 ∈ H01 (Ω) and Ω C R3 is a smooth bounded domain. We are interested in existence and multiplicity of solutions depending on the parameters p and λ. Our results extend previous work made in R3
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