In this paper, we investigate the existence of ground state solutions for a class of Kirchhoff equation involving the fractional Laplacian and Hartree-type nonlinearity{(a+b∫R3|(−Δ)s2u|2dx)(−Δ)su+V(x)u=(Iμ⁎|u|p)|u|p−2uin R3,u∈Hs(R3), where a,b>0 are constants, μ∈(4s−3,3), s∈(34,1), p∈(3+μ3,3+μ3−2s), Iμ denotes the Riesz potential, and (−Δ)s stands for the fractional Laplacian. Firstly, we establish the existence of Pohozaev-type ground state solutions for the equation with the constant potential V(x). Building upon this result, we further apply appropriate analytical techniques to prove the existence of such ground state solutions for the equation with a general potential V(x).
We prove that the set of integrable functions on the unit circle for which the analogue of Paley's theorem for H1 fails is residual in L1(T). Moreover, we establish algebraic genericity and spaceability results in several Hardy-type function spaces under prescribed conditions on Taylor coefficients, extending phenomena considered in [12], [15].
Given a bounded linear operator A on a Banach space, Kreiss and Tadmor-Ritt are two well-known resolvent conditions related to power-boundedness of A, that is, ‖Ak‖ is bounded by some M(A) for all k≥0. The classical Kreiss matrix theorem gives a finite-dimensional characterization up to a dimension-dependent constant. This dependence on dimension makes the theorem unsuitable as a Banach-space criterion. One main goal of this paper is to introduce a Banach-space version of the Kreiss constant that is equivalent to M(A) for all power-bounded operators A. For a Tadmor-Ritt operator A, one has M(A)≤CT(A)log(1+T(A)). We show that the log term cannot be removed in general, resolving a conjecture that has been open for 23 years.
Given an analytic function g on the unit disk D, we investigate analytic paraproduct operators associated with g, given byTgf(z)=∫0zf(ζ)g′(ζ)dζ,Sgf(z)=∫0zf′(ζ)g(ζ)dζ, andMgf(z)=f(z)g(z). Our interest lies in characterizing the boundedness of operators belonging to the algebra Ag generated by Tg, Sg, and Mg on weighted mixed norm spaces over the unit disk. These general problems turn out to be highly nontrivial: elements of Ag are finite linear combinations of finite products (words) of the three fundamental operators, and delicate cancellation effects arise when analyzing such products. The results in [2] show that a complete quantitative characterization of the boundedness of an arbitrary word in Ag on Hardy and Bergman spaces can be provided in the form of a fractional power of the symbol g, and the boundedness depends only on the number of occurrences of each letter Tg, Sg, and Mg in a given word. This paper makes progress in this direction in mixed norm spaces. Our main result provides a complete quantitative characterization of the boundedness of words in Ag for n∈N0:=N∪{0} in the form of “fractional powers” of the symbol g, which boundedness depends only on the number of occurrences of each letter Tg, Sg, and Mg in a given word.
In this paper, we investigate the output feedback stabilization of wave equation with Van Der Pol type boundary condition and disturbance. By expanding interactive integral control, we propose a novel method to compensate for disturbance by using non-collocated boundary measurements. Based on this method, we design two types of dynamic feedback control laws to stabilize the system. Afterwards, the numerical experiments are carried out to illustrate the proposed approach.
Frequent pest outbreaks seriously threaten the sustainable production of global agriculture. Existing integrated pest management (IPM) models fail to adequately characterize the periodic switching of pests between incomplete-hiding and complete-exposure behaviors, and rarely incorporate both pest fear effects and intraspecific cooperative hunting of natural enemies. This paper constructs a periodically switched impulsive pest-natural enemy dynamical model, in which Holling-type functional responses with cooperative hunting are adopted for both pest behavioral stages. The coefficient (1−β) is introduced to describe the decay of pests' effective exposure fraction in the incomplete-hiding stage, and an additional fear effect is imposed in the complete-exposure phase to suppress pest reproduction. Combined with pest behavioral rhythms, behavior-adaptive impulsive control strategies are designed: pesticide spraying is performed at the phase-switching instant, and density-dependent supplementary release of natural enemies is implemented at the end of each full period. Based on impulsive comparison theorems and Floquet theory, we obtain the critical threshold I0: the pest-extinction periodic solution is globally asymptotically stable (GAS) when I0<1, and the system is uniformly permanent when I0>1. LHS-PRCC sensitivity analysis shows that the incomplete-hiding proportion raises the pest-extinction threshold I0, whereas natural-enemy release intensity and cooperative-hunting behavior reduce I0. Numerical simulations verify that the system exhibits complex dynamics including period-doubling bifurcations, chaos and multistability, triggering state transitions between pest extinction and population coexistence. This work provides theoretical support for ecologically friendly integrated pest management strategies.
We prove an integral-form almost sure central limit theorem for nonlinear functionals of Gaussian fields, with weight functions that satisfy continuous analogues of Hörmann's conditions. The proof relies on a new criterion in terms of Kolmogorov, total variation, and Wasserstein distances adapted from the Ibragimov–Lifshits method, which can be verified using Malliavin calculus. As applications, we establish the almost sure central limit theorem for the quadratic variations of fractional, sub-fractional, and tempered fractional Brownian motion.
In this paper, we prove that the symmetric Banach space L1∩L∞ has the Mazur-Ulam property. That is, every surjective isometry V:S(L1∩L∞)→S(F) admits an extension to a surjective linear isometry from L1∩L∞ onto F, where F is an arbitrary Banach space.
Let u and v be plurifine plurisubharmonic functions. In this paper, we investigate sufficient conditions on u and v under which they can be compared.
This work introduces a real representation of reduced biquaternion matrices and proposes reduced biquaternion biconjugate residual (RBBCR) algorithm for addressing coupled reduced biquaternion matrix equations. It rigorously proves the convergence of the RBBCR algorithm. To assess performance, numerical experiments are conducted to verify its efficiency. Furthermore, RBBCR algorithm is applied to color image encryption problem.
This paper is devoted to the asymptotic analysis of the first-order ordinary differential equations: y′(t)=f(t+x0,y(t)) with y(0)=y0, such that the planar flow Φ associated with the vector field (1,f) has a first integral σ. On the one hand, assuming some inf-sup condition satisfied by σ combined with some regime satisfied by (x0,y0), we prove that the solution y is bounded in R. On the other hand, when the functions f, ∂xσ, ∂yσ are Z2-periodic and ∂yσ does not vanish in R2, we prove that the limit of y(t)/t as |t|→∞ does exist and is expressed by the mean-values of ∂xσ, ∂yσ independently of the point (x0,y0). The key-ingredient of these asymptotic results is the derivation of two classes of invariant functions for the flow Φ in the whole space R2, which induce explicit first integrals σ for the flow. The periodic framework is more delicate, since we establish a necessary and sufficient condition for the existence of a first integral. The results are illustrated by various examples along the paper.
