177,795 research outputs found
Positive solutions for some non-autonomous Schrödinger–Poisson systems
No full textAbstractIn this paper we study the Schrödinger–Poisson system(SP){−Δu+u+K(x)ϕ(x)u=a(x)|u|p−1u,x∈R3,−Δϕ=K(x)u2,x∈R3, with p∈(3,5). Assuming that a:R3→R and K:R3→R are nonnegative functions such thatlim|x|→∞a(x)=a∞>0,lim|x|→∞K(x)=0 and satisfying suitable assumptions, but not requiring any symmetry property on them, we prove the existence of positive solutions
Correction to: Epidemiological, otolaryngological, olfactory and gustatory outcomes according to the severity of COVID-19: a study of 2579 patients
No full textIn the original publication of the article, one of the co-author’s name was published incorrectly as “Liugi A. Varia”. The correct name should read as “Luigi A. Vaira”
Sign-changing blowing-up solutions for the Brezis-Nirenberg problem in dimensions four and five
No full textWe consider the Brezis-Nirenberg problem:
where is a smooth bounded domain in , , and lambda>0.
In this paper we prove that, if is symmetric and , there exists a sign-changing solution whose positive part concentrates and blows-up at the center of symmetry of the domain, while the negative part vanishes, as , where denotes the first eigenvalue of on , with zero Dirichlet boundary condition
Non-radial sign-changing solutions for the Schrödinger–Poisson problem in the semiclassical limit
No full textWe study the following system of equations known as Schrödinger–Poisson problem (Formula Presented) where ε>0 is a small parameter, f:R→R is given, N ≥ 3 , aN is the surface measure of the unit sphere in RN and the unknowns are υ,φ:RN→R. We construct non-radial sign-changing multi-peak solutions in the semiclassical limit. The peaks are displaced in suitable symmetric configurations and collapse to the same point as ε→ 0. The proof is based on the Lyapunov–Schmidt reduction
Non-radial sign-changing solutions for the Schrödinger–Poisson problem in the semiclassical limit
No full textWe study the Schroedinger– Poisson problem
in R^N and construct non-radial sign-changing multi-peak solutions in the semiclassical limit. The peaks are displaced in suitable symmetric configurations and collapse to the same point as the parameter ε → 0. The proof is based on the Lyapunov–Schmidt reduction
Cluster solutions for the schrödinger-poisson-slater problem around a local minimum of the potential
No full textIn this paper we consider the system in R 3(0.1) -ε 2 Δu + V(x)u + Φ(x)u = u p, -ΔΦ = u 2, for p ε (1, 5). We prove the existence of multi-bump solutions whose bumps concentrate around a local minimum of the potential V(x). We point out that such solutions do not exist in the framework of the usual Nonlinear Schrödinger Equation
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