200 research outputs found
Multiple and least energy sign-changing solutions for Schrodinger-Poisson equations in R3 with restraint
In this paper, we study the existence of multiple sign-changing solutions with a prescribed Lp+1−norm and theexistence of least energy sign-changing restrained solutions for the following nonlinear Schr¨odinger-Poisson system:By choosing a proper functional restricted on some appropriate subset to using a method of invariant sets of descending flow,we prove that this system has infinitely many sign-changing solutions with the prescribed Lp+1−norm and has a least energy forsuch sign-changing restrained solution for p ∈ (3, 5). Few existence results of multiple sign-changing restrained solutions areavailable in the literature. Our work generalize some results in literature
Sign-changing solutions for a Schrödinger-Kirchhoff-Poisson system with 4-sublinear growth nonlinearity
In this paper we consider the following Schrödinger–Kirchhoff–Poisson-type system where Ω is a bounded smooth domain of R3 , a > 0, b ≥ 0 are constants and λ is a positive parameter. Under suitable conditions on Q(x) and combining the method of invariant sets of descending flow, we establish the existence and multiplicity of signchanging solutions to this problem for the case that 2 < p < 4 as λ sufficiently small. Furthermore, for λ = 1 and the above assumptions on Q(x), we obtain the same conclusions with 2 < p < 12 5
A guide to the Choquard equation
We survey old and recent results dealing with the existence and properties of
solutions to the Choquard type equations and some of its variants and extensions.Comment: 39 page
Existence of positive solutions to Kirchhoff type problems with zero mass
The existence of positive solutions depending on a nonnegative parameter lambda to Kirchhoff type problems with zero mass is proved by using variational method, and the new result does not require usual compactness conditions. A priori estimate and a Pohozaev type identity are used to obtain the bounded Palais-Smale sequences for constant coefficient nonlinearity, while a cut-off functional and Pohozaev type identity are utilized to obtain the bounded Palais-Smale sequences for the variable-coefficient case. (C) 2013 Elsevier Inc. All rights reserved
The Choquard logarithmic equation involving a nonlinearity with exponential growth
In the present work we are concerned with the Choquard Logarithmic equation
in ,
for , and a nonlinearity with exponential critical
growth. We prove the existence of a nontrivial solution at the mountain pass
level and a nontrivial ground state solution. Also, we provide these results
under a symmetric setting, taking into account subgroups of
Astrophysical Searches and Constraints on Ultralight Bosonic Dark Matter
Starting from the evidence that dark matter indeed exists and permeates the
entire cosmos, various bounds on its properties can be estimated. Beginning
with the cosmic microwave background and large scale structure, we summarize
bounds on the ultralight bosonic dark matter (UBDM) mass and cosmic density.
These bounds are extended to larger masses by considering galaxy formation and
evolution, and the phenomenon of black hole superradiance. We then discuss the
formation of different classes of UBDM compact objects including solitons/axion
stars and miniclusters. Next, we consider astrophysical constraints on the
couplings of UBDM to Standard Model particles, from stellar cooling (production
of UBDM) and indirect searches (decays or conversion of UBDM). Throughout,
there are short discussions of "hints and opportunities" in searching for UBDM
in each area.Comment: 46 pages, 8 figures. To appear as Chapter 3 in "The Search for
Ultralight Bosonic Dark Matter," edited by Derek F. Jackson Kimball & Karl
van Bibber (Springer, 2021). Solutions for the problems are include
Modeling of ultrashort optical pulses in nonlinear fibers
This work deals with theoretical aspects of pulse propagation. The core focus is on extreme, few-cycle pulses in optical fibers, pulses that are strongly affected by both dispersion and nonlinearity. Using Hamil- tonian methods, we discuss how the meaning of pulse envelope changes, as pulses become shorter and shorter, and why an envelope equation can still be used. We also discuss how the standard set of dispersion coefficients yields useful rational approximations for the chromatic dispersion in optical fibers. Three more specific problems are addressed thereafter. First, we present an alternative framework for ultra- short pulses in which non-envelope propagation models are used. The approach yields the limiting, shortest solitons and reveals their universal features. Second, we describe how one can manipulate an ultrashort pulse, i.e., to change its amplitude and duration in a predictable manner. Quantitative theory of the manipu- lation is presented based on perturbation theory for solitons and analogy between classical fiber optics and quantum mechanics. Last but not least, we consider a recently found alternative to the standard split-step approach for numerical solutions of the pulse propagation equations
- …