Existence and limiting behavior of minimizers for attractive Schrödinger‐Poisson systems with periodic potentials
Sign Up to like & getrecommendations! Published in 2020 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.6232
Abstract: We study the constrained minimizing problem of the energy functional related to attractive Schrödinger‐Poisson systems with periodic potentials: I(m)=infE(ϕ):ϕ∈H1(R3),‖ϕ‖L22=m, where E(ϕ):=12∫R3|∇ϕ(x)|2dx+12∫R3V(x)|ϕ(x)|2dx−14∬R3×R3|ϕ(x)|2|ϕ(y)|2|x−y|dxdy−1α+2∫R3|ϕ(x)|α+2dx, with m>0 , α>0 , and V is a continuous periodic potential. We first… read more here.
Keywords: poisson systems; dinger poisson; attractive schr; systems periodic ... See more keywords
Nodal solutions for Schrödinger-Poisson systems with concave-convex nonlinearities
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2021.125006
Abstract: Abstract In this paper, we study the existence of nodal solutions for the Schrodinger-Poisson systems with concave-convex nonlinearities (0.1) { − Δ u + ϕ u = λ | u | p − 2 u… read more here.
Keywords: concave convex; systems concave; solutions schr; nodal solutions ... See more keywords
From optics to dark matter: A review on nonlinear Schrödinger–Poisson systems
Sign Up to like & getrecommendations! Published in 2020 at "Physica D: Nonlinear Phenomena"
DOI: 10.1016/j.physd.2019.132301
Abstract: Abstract We review recent progress in Schrodinger–Poisson systems in 1+2 and 1+3 dimensions in the presence of nonlinear terms. In a mean field approach, this mathematical model describes the semiclassical behavior of an N -body… read more here.
Keywords: optics; poisson systems; dark matter; review ... See more keywords
Least energy solutions for a class of fractional Schrödinger-Poisson systems
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DOI: 10.1063/1.5047663
Abstract: In this paper, the existence of a nontrivial least energy solution is considered for the nonlinear fractional Schrodinger-Poisson systems (−Δ)su + V(x)u + ϕu = |u|p−1u and (−Δ)tϕ = u2 in R3, where (−Δ)α is… read more here.
Keywords: energy; poisson systems; nontrivial least; least energy ... See more keywords
Nehari type ground state solutions for periodic Schrödinger–Poisson systems with variable growth
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DOI: 10.1080/17476933.2020.1843643
Abstract: In this paper, we deal with the variable growth Schrodinger–Poisson Systems in R 3 : − d i v ( | ∇ u | p ( x ) − 2 ∇ u ) + (… read more here.
Keywords: type ground; poisson systems; nehari type; variable growth ... See more keywords
THE FRACTIONAL SCHRÖDINGER-POISSON SYSTEMS WITH INFINITELY MANY SOLUTIONS
Sign Up to like & getrecommendations! Published in 2020 at "Journal of The Korean Mathematical Society"
DOI: 10.4134/jkms.j190156
Abstract: . In this paper, we study the existence of infinitely many large energy solutions for the supercubic fractional Schr¨odinger-Poisson sys- tems. We consider different superlinear growth assumptions on the nonlinearity, starting from the well-know Ambrosetti-Rabinowitz… read more here.
Keywords: schr dinger; dinger poisson; poisson; poisson systems ... See more keywords