37 research outputs found
Computations of critical groups and periodic solutions for asymptotically linear Hamiltonian systems
AbstractThe purpose of this paper is two-fold. Firstly, we will give some parabolic-like conditions which improve the well-known angle conditions and allow further computations of the critical groups both at degenerate critical points and at infinity. As an application, we then consider the second-order Hamiltonian systemsu″(t)+∇H(t,u(t))=0,t∈R, where H:R×RN→R is T-periodic in its first variable and ∇H is asymptotically linear both at origin and at infinity. Based on the computations of the critical groups and the Morse theory, we obtain the existence and multiplicity results for periodic solutions under new classes of conditions. It turns out that our main results improve sharply some known results in the literature
Normalized solutions for the Choquard equation with mass supercritical nonlinearity
We consider the nonlinear Choquard equation where
, is prescribed, is a Lagarange
multiplier, and is the Riesz potential.
Under general assumptions on the nonlinearity we prove the existence and
multiplicity of normalized solutions.Comment: arXiv admin note: text overlap with arXiv:2002.03973 by other author
Asymptotic profiles for a nonlinear Kirchhoff equation with combined powers nonlinearity
We study asymptotic behavior of positive ground state solutions of the
nonlinear Kirchhoff equation as and ,
where or , , is the Sobolev
critical exponent, , are constants and is a
parameter. In particular, we prove that in the case , as , after a suitable rescaling the ground state solutions of the problem
converge to the unique positive solution of the equation
and as , after another rescaling the ground state solutions
of the problem converge to a particular solution of the critical Emden-Fowler
equation . We establish a sharp asymptotic
characterisation of such rescalings, which depends in a non-trivial way on the
space dimension and . We also discuss a connection of our results
with a mass constrained problem associated to the Kirchhoff equation with the
mass normalization constraint .Comment: 40 page
Semilinear Duffing Equations Crossing Resonance Points
AbstractIn this paper, using a generalized form of the Poincaré–Birkhoff theorem and a fixed point theorem, we prove, under weaker conditions, two theorems for the equationx+g(x)=p(t),p(t)≡p(t+2π), of which one shows the existence of a harmonic solution, the other that the equation may have an infinite number of harmonic solutions in the resonance case. This is an enhancement of the results already obtained
Propagation and its failure in a lattice delayed differential equation with global interaction
AbstractWe study the existence, uniqueness, global asymptotic stability and propagation failure of traveling wave fronts in a lattice delayed differential equation with global interaction for a single species population with two age classes and a fixed maturation period living in a spatially unbounded environment. In the bistable case, under realistic assumptions on the birth function, we prove that the equation admits a strictly monotone increasing traveling wave front. Moreover, if the wave speed does not vanish, then the wave front is unique (up to a translation) and globally asymptotic stable with phase shift. Of particular interest is the phenomenon of “propagation failure” or “pinning” (that is, wave speed c = 0), we also give some criteria for pinning in this paper
Traveling Wave Solutions for Planar Lattice Differential Systems with Applications to Neural Networks
AbstractWe obtain some existence results for traveling wave fronts and slowly oscillatory spatially periodic traveling waves of planar lattice differential systems with delay. Our approach is via Schauder's fixed-point theorem for the existence of traveling wave fronts and via S1-degree and equivarant bifurcation theory for the existence of periodic traveling waves. As examples, the obtained abstract results will be applied to a model arising from neural networks and explicit conditions for traveling wave fronts and global continuation of periodic waves will be obtained
COMPARATIVE STUDY OF ON-SITE SORTING FOR C&D IN CHINA AND EUROPE
Construction and demolition waste (CDW) accounts for 40% of urban municipal waste in China and around 25% in the European Union (EU). Since the EU is more developed and urbanized than China, its experience with managing CDW may be helpful to China. This study therefore compared China and the EU with respect to the flow of CDW materials and the policies, laws and regulations for CDW management. The results reveal that the CDW management practices and facilities in China are relatively underdeveloped with a large amount of low-value inert material going to landfill compared with the EU. The study also reveals the important role of government involvement in CDW management, including the use of punitive measures and preferential policies; most EU members states achieved their waste recovery rates by 2016 due to mature CDW legalization. To improve the management of CDW in China, a series of suggestions are proposed including waste prevention strategies, establishment of supervision mechanisms, and financial support. </jats:p
Infinitely Many Nontrivial Solutions of Resonant Cooperative Elliptic Systems with Superlinear Terms
We study a class of resonant cooperative elliptic systems and replace the Ambrosetti-Rabinowitz superlinear condition with general superlinear conditions. We obtain ground state solutions and infinitely many nontrivial solutions of this system by a generalized Nehari manifold method developed recently by Szulkin and Weth