continuous pole placement for delay equations in this paper we describe a stabilization method for linear time delay systems which extends the classical pole placement method for ordinary differential equations unlike methods based on finite spectrum assignment our method does not render the closed loop system finite dimensional but consists of controlling the rightmost eigenvalues because these are moved to the left half plane in a quasi continuous way we refer to our method as continuous pole placement we explain the method by means of the stabilization of a linear finite dimensional system in the presence of an input delay and illustrate its applicability to more general stabilization problems

locally conformal kahler manifolds with potential a locally conformally kahler lck manifold m is one which is covered by a kahler manifold widetilde m with the deck transformation group acting conformally on widetilde m if m admits a holomorphic flow acting on widetilde m conformally it is called a vaisman manifold neither the class of lck manifolds nor that of vaisman manifolds is stable under small deformations we define a new class of lck manifolds called lck manifolds with potential which is closed under small deformations all vaisman manifolds are lck with potential we show that an lck manifold with potential admits a covering which can be compactified to a stein variety by adding one point this is used to show that any lck manifold m with potential dim m 3 can be embedded into a hopf manifold thus improving similar results for vaisman manifolds ornea and verbitsky math ann 332 121 143 2005

a multiplicity result for a nonlinear fractional schrodinger equation in rn without the ambrosetti rabinowitz condition abstract in this paper we study the existence and the multiplicity of positive solutions for the following class of fractional schrodinger equations 2 s s u v x u f u in r n where 0 is a parameter s 0 1 n 2 s v r n r is a continuous positive potential and f r r is a c 1 superlinear nonlinearity which does not satisfy the ambrosetti rabinowitz condition the main result is established by using minimax methods and ljusternik schnirelmann theory of critical points

uniqueness of non linear ground states for fractional laplacians in mathbb r we prove uniqueness of ground state solutions q q x 0 of the non linear equation sq q q 1 0inr s q q q 1 0 i n r where 0 s 1 and 0 4s 1 2s for s 12 s 1 2 and 0 for s 12 s 1 2 here s denotes the fractional laplacian in one dimension in particular we answer affirmatively an open question recently raised by kenig martel robbiano and we generalize by completely different techniques the specific uniqueness result obtained by amick and toland for s 12 s 1 2 and 1 in 5 for the benjamin ono equation as a technical key result in this paper we show that the associated linearized operator l s 1 1 q is non degenerate i e its kernel satisfies ker l span q this result about l proves a spectral assumption which plays a central role for the stability of solitary waves and blowup analysis for non linear dispersive pdes with fractional laplacians such as the generalized benjamin ono bo and benjamin bona mahony bbm water wave equations

an intrinsic characterization of kahler manifolds on etudie la condition de kahler pour une variete complexe compacte on caracterise les varietes complexes compactes qui admettent des metriques de kahler

stability of semiclassical bound states of nonlinear schrodinger equations with potentials in this paper we study the lyapunov stabilities of some semiclassical bound states of the nonhomogeneous nonlinear schrodinger equation we prove that among those bound states those which are concentrated near local minima respectively maxima of the potentialv are stable respectively unstable we also prove that those bound states are positive if is sufficiently small

on a fractional schrodinger equation with periodic potential abstract in this paper we first consider the spectrum of the fractional schrodinger operator s v x on r n where s 0 1 and v x be continuous periodic in x using a new nonlocal normal derivative we prove that the operator has purely continuous spectrum which is bounded below and consists of closed disjoint intervals then when 0 belongs to a spectral gap of s v x we establish an existence result for the fractional schrodinger equation via a new linking theorem it is worth to mention that the nonlinear term in our problem does not satisfy the periodicity and the existence result is even new for the case s 1

complex geometry of moment angle manifolds moment angle manifolds provide a wide class of examples of non kahler compact complex manifolds a complex moment angle manifold mathcal z is constructed via certain combinatorial data called a complete simplicial fan in the case of rational fans the manifold mathcal z is the total space of a holomorphic bundle over a toric variety with fibres compact complex tori in general a complex moment angle manifold mathcal z is equipped with a canonical holomorphic foliation mathcal f which is equivariant with respect to the mathbb c times m action examples of moment angle manifolds include hopf manifolds of vaisman type calabi eckmann manifolds and their deformations we construct transversely kahler metrics on moment angle manifolds under some restriction on the combinatorial data we prove that any kahler submanifold or more generally a fujiki class mathcal c subvariety in such a moment angle manifold is contained in a leaf of the foliation mathcal f for a generic moment angle manifold mathcal z in its combinatorial class we prove that all subvarieties are moment angle manifolds of smaller dimension and there are only finitely many of them this implies in particular that the algebraic dimension of mathcal z is zero

brief paper leader following consensus of second order agents with multiple time varying delays in this paper a leader following consensus problem of second order multi agent systems with fixed and switching topologies as well as non uniform time varying delays is considered for the case of fixed topology a necessary and sufficient condition is obtained for the case of switching topology a sufficient condition is obtained under the assumption that the total period over which the leader is globally reachable is sufficiently large we not only prove that a consensus is reachable asymptotically but also give an estimation of the convergence rate an example with simulation is presented to illustrate the theoretical results

semiclassical states for weakly coupled fractional schrodinger systems abstract in this paper we consider the nonlinear system of two weakly coupled fractional schrodinger equations with nonconstant potentials e 2 s s u p 1 x u u 2 p b u p 1 v p 1 u x r n e 2 s s v p 2 x v v 2 p b v p 1 u p 1 v x r n we investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials

on the disk theorem we construct an example of a 2 dimensional stein normal space x with one singular point x0 such that x x0 is simply connected and it satisfies the disk condition this answers a question raised by fornaess and narasimhan we also prove that any increasing union of stein open sets contained in a stein space of dimension 2 satisfies the disk condition starting from the above example we exhibit without using deformation theory a new type of 2 dimensional holes which cannot be filled

on the metric structure of non kahler complex surfaces we give a characterization of a locally conformally kahler l c k metric with parallel lee form on a compact complex surface using the kodaira classification of surfaces we classify the compact complex surfaces admitting such structures this gives a classification of sasakian structures on compact three manifolds a weak version of the above mentioned characterization leads to an explicit construction of l c k metrics on all hopf surfaces we characterize the locally homogeneous l c k metrics on geometric complex surfaces and we prove that some inoue surfaces do not admit any l c k metric

ground state and bounded state solution for the nonlinear fractional choquard schrodinger poisson system in this paper we study a class of fractional choquard schrodinger poisson system under some suitable assumptions by using a variational approach we establish the existence of non negative ground state solution and also discuss the nonexistence of ground states moreover we prove the existence of bounded state by using a linking theorem

multiplicity of semiclassical states for fractional schrodinger equations with critical frequency abstract we are concerned with the fractional schrodinger equation 2 u v x u u 2 2 u x r n where 0 is a parameter 0 1 n 3 2 2 n n 2 v l n 2 r n is a nonnegative function and v is assumed to be zero in some region of r n which means it is of the critical frequency case by virtue of a global compactness lemma two barycenter functions and lusternik schnirelman theory we show the multiplicity of high energy semiclassical states

semiclassical states for fractional schrodinger equations with critical growth abstract in this paper we consider the following fractional nonlinear schrodinger equations e 2 s s u v x u p x g u q x u 2 s 2 u x r n and prove the existence and concentration of positive solutions under suitable assumptions on the potentials v x p x and q x we show that the semiclassical solutions u e with maximum points x e concentrating at a special set s p characterized by v x p x and q x moreover for any sequence x e x 0 s p v e x u e e x x e convergence strongly in h s r n to a ground state solution v of s v v x 0 v p x 0 g v q x 0 v 2 s 2 v x r n

solutions of the fractional schrodinger equation with a sign changing nonlinearity abstract we look for solutions to a nonlinear fractional schrodinger equation 2 u v x u f x u x u q 2 u on r n where the potential v is coercive or v v p e r v l o c is a sum of a periodic in x potential v p e r and a localized potential v l o c l r n is periodic in x x 0 for a e x r n and 2 q 2 if f has the subcritical growth but higher than x u q 2 u then we find a ground state solution being a minimizer on the nehari manifold moreover we show that if f is odd in u and v is periodic this equation admits infinitely many solutions which are pairwise geometrically distinct finally we obtain the existence result in the case of coercive potential v

consensus conditions of continuous time multi agent systems with time delays and measurement noises this work is concerned with stochastic consensus conditions of multi agent systems with both time delays and measurement noises for the case of additive noises we develop some necessary conditions and sufficient conditions for stochastic weak consensus by estimating the differential resolvent function for delay equations by the martingale convergence theorem we obtain necessary conditions and sufficient conditions for stochastic strong consensus for the case of multiplicative noises we consider two kinds of time delays appeared in the measurement term and the noise term respectively we first show that stochastic weak consensus with the exponential convergence rate implies stochastic strong consensus then by constructing degenerate lyapunov functional we find the sufficient consensus conditions and show that stochastic consensus can be achieved by carefully choosing the control gain according to the noise intensities and the time delay in the measurement term

mas consensus and delay limits under delayed output feedback in this technical note we study the consensus problem for discrete time multi agent systems over an undirected fixed network communication graph focusing on the robustness of consensus with respect to communication delay we assume that the agents input is subject to a constant albeit possibly unknown time delay and is generated by a distributed dynamic output feedback control protocol drawing upon concepts and techniques from robust control notably those concerning gain margin optimization and analytic interpolation we derive explicit closed form conditions for general linear agents to achieve consensus our results display an explicit dependence of the consensus condition on the delay value as well as on the agent s unstable poles and non minimum phase zeros showing that delayed communication between agents will generally hinder consensus and impose restrictions on the network topology we also show that a lower bound on the maximal delay allowable for consensus can be computed by a simple line search method

input delay margin for consensusability of multi agent systems in this paper we are concerned with the consensus of multi agent systems with input delay among all standard static protocols that achieve the consensus for the multi agent system under no input delay we aim to find the maximum input delay such that the system remains consensusable under the same protocols in the case of continuous time systems in view of the continuity of stability with respect to the time delay the maximum delay margin for consensusability is given for scalar systems and vector systems with a single unstable open loop pole for scalar discrete time systems we show that the maximum delay margin for consensusability is strictly greater than zero if and only if the open loop pole of the system is located in a specified interval

concentration phenomena for a class of fractional kirchhoff equations in rn with general nonlinearities abstract in this paper we study the following class of fractional kirchhoff problems e 2 s m e 2 s n u s 2 s u v x u f u in r n u h s r n u 0 in r n where e 0 is a small parameter s 0 1 n 2 s is the fractional laplacian v r n r is a positive continuous function m 0 r is a kirchhoff function satisfying suitable conditions and f r r fulfills berestycki lions type assumptions of subcritical or critical type using suitable variational arguments we prove the existence of a family of positive solutions u e which concentrates at a local minimum of v as e 0

on the compactification of hyperconcave ends and the theorems of siu yau and nadel we show that the pseudoconcave holes of some naturally arising class of manifolds called hyperconcave ends can be filled in including the case of complex dimension two as a consequence we obtain a stronger version of the compactification theorem of siu yau and extend nadel s theorems to dimension two

a local mountain pass approach for a class of fractional nls equations with magnetic fields abstract we complete the recent study started in ambrosio 2019 concerning the existence and concentration phenomenon of complex valued solutions for a class of nonlinear schrodinger equations driven by the fractional magnetic laplacian a s the proofs are obtained by combining suitable variational methods with a kato s approximation argument for a s the approach developed here can be also used to consider other fractional magnetic problems like fractional magnetic choquard equations fractional magnetic kirchhoff problems and fractional magnetic schrodinger poisson equations in which local conditions on the potential are assumed

compactification of complete kahler manifolds of negative ricci curvature soit m une variete de kahler complete de dimension m et soit la forme de kahler on suppose 1 ric 0 2 m est tres fortement m 2 pseudoconcave 3 le recouvrement universel de m est de stein alors m est biholomorphe a une variete quasiprojective

a non compactness result on the fractional yamabe problem in large dimensions abstract let x n 1 g be an n 1 dimensional asymptotically hyperbolic manifold with conformal infinity m n h the fractional yamabe problem addresses to solve p g h u c u n 2 n 2 u 0 on m where c r and p g h is the fractional conformal laplacian whose principal symbol is the laplace beltrami operator on m in this paper we construct a metric on the half space x r n 1 which is conformally equivalent to the unit ball for which the solution set of the fractional yamabe equation is non compact provided that n 24 for 0 and n 25 for 1 where 0 1 is a certain transition exponent the value of turns out to be approximately 0 940197

a critical nonlinear fractional elliptic equation with saddle like potential in ℝn in this paper we study the existence of positive solution for the following class of fractional elliptic equation 2s su v z u uq 2u u2s 2uinrn where 0 are positive parameters q 2 2s 2s 2nn 2s n 2s s 0 1 su is the fractional laplacian and v is a saddle like potential the result is proved by using minimizing method constrained to the nehari manifold a special minimax level is obtained by using an argument made by benci and cerami

when is the achievable discrete time delay margin nonzero this technical note considers the delay margin problem for discrete time finite dimensional linear time invariant fdlti single input single output siso systems this problem has been studied extensively in continuous time it is well known that given a fdlti plant and controller forming a strictly proper stable feedback connection closed loop stability will be maintained for small delays hence the achievable delay margin using fdlti control is strictly greater than zero in this work we show that this is not the case for discrete time systems indeed we show that a fdlti siso discrete time plant has an achievable delay margin strictly greater than zero if and only if it has no negative real unstable poles

the method weak lefschetz theorems and the topology of kahler manifolds in no nori studied the fundamental group of complements of nodal curves with ample normal bundle in smooth projective surfaces the main tool was the following weak lefschetz theorem theorem nori suppose u x is a local biholomorphism from a connected complex manifold u into a connected smooth projective variety x of dimension at least 2 and u contains a connected effective divisor y with compact support and ample normal bundle then for every zariski open subset z of x the image of 1 1 z in 1 z is of finite index

time varying low gain feedback for linear systems with unknown input delay abstract in this paper the traditional low gain feedback design with a time invariant feedback parameter is generalized to time varying parameter design for linear systems with delayed input for an unknown delay with a known upper bound a time varying low gain feedback law constructed by using the parametric lyapunov equation based approach globally regulates a system with all open loop poles at the origin as long as the time varying low gain parameter has a continuous second derivative and approaches a sufficiently small constant with its derivative approaching zero as time goes to infinity improvement of the closed loop performance is addressed in a convergence rate analysis and then observed in simulation compared with the traditional constant parameter low gain design

global bifurcation results for a fractional equation in rn abstract in this paper we study the existence of positive solution for the following class of fractional equation p s u g x f u in r n 0 u x 1 x r n lim x u x 0 where n 2 s s 0 1 0 f r r is a continuous function g r n r is a bounded continuous function that changes sign and s u is the fractional laplacian the main tools used are a theorem due to crandall and rabinowitz 14 and the global bifurcation theorem due to rabinowitz 23

nonlocal scalar field equations qualitative properties asymptotic profiles and local uniqueness of solutions abstract we study the nonlocal scalar field equation with a vanishing parameter p s u u u p 2 u u q 2 u in r n u h s r n where s 0 1 n 2 s q p 2 are fixed parameters and 0 is a vanishing parameter for small we prove the existence and qualitative properties of positive solutions next we study the asymptotic behavior of ground state solutions when p is subcritical supercritical or critical sobolev exponent 2 2 n n 2 s for p 2 the ground state solution asymptotically coincides with unique positive ground state solution of s u u u p whereas for p 2 the asymptotic behavior of the solutions is given by the unique positive solution of the nonlocal critical emden fowler type equation for p 2 the solution asymptotically coincides with a ground state solution of s u u p u q furthermore using these asymptotic profile of positive solutions we establish the local uniqueness of positive solution

uniqueness of radial solutions for the fractional laplacian we prove general uniqueness results for radial solutions of linear and nonlinear equations involving the fractional laplacian s with s 0 1 for any space dimensions n 1 by extending a monotonicity formula found by cabre and sire we show that the linear equation s u vu 0 in r n has at most one radial and bounded solution vanishing at infinity provided that the potential v is radial and nondecreasing in particular this result implies that all radial eigenvalues of the corresponding fractional schrodinger operator h s v are simple furthermore by combining these findings on linear equations with topological bounds for a related problem on the upper half space r n 1 we show uniqueness and nondegeneracy of ground state solutions for the nonlinear equation s q q q q 0 in r n for arbitrary space dimensions n 1 and all admissible exponents 0 this generalizes the nondegeneracy and uniqueness result for dimension n 1 recently obtained by the first two authors and in particular the uniqueness result for solitary waves of the benjamin ono equation found by amick and toland

embeddability of some strongly pseudoconvex cr manifolds we obtain an embedding theorem for compact strongly pseudoconvex cr manifolds which are boundaries of some complete hermitian manifolds we use this to compactify some negatively curved kahler manifolds with compact strongly pseudoconvex boundary an embedding theorem for sasakian manifolds is also derived

network topology and communication data rate for consensusability of discrete time multi agent systems this paper investigates the joint effect of agent dynamic network topology and communication data rate on consensusability of linear discrete time multi agent systems neglecting the finite communication data rate constraint and under undirected graphs a necessary and sufficient condition for consensusability under a common control protocol is given which explicitly reveals how the intrinsic entropy rate of the agent dynamic and the communication graph jointly affect consensusability the result is established by solving a discrete time simultaneous stabilization problem a lower bound of the optimal convergence rate to consensus which is shown to be tight for some special cases is provided as well moreover a necessary and sufficient condition for formationability of multi agent systems is obtained as a special case the discrete time second order consensus is discussed where an optimal control gain is designed to achieve the fastest convergence the effects of undirected graphs on consensability formationability and optimal convergence rate are exactly quantified by the ratio of the second smallest to the largest eigenvalues of the graph laplacian matrix an extension to directed graphs is also made the consensus problem under a finite communication data rate is finally investigated

fractional schrodinger equation some properties of the fractional schrodinger equation are studied we prove the hermiticity of the fractional hamilton operator and establish the parity conservation law for fractional quantum mechanics as physical applications of the fractional schrodinger equation we find the energy spectra of a hydrogenlike atom fractional bohr atom and of a fractional oscillator in the semiclassical approximation an equation for the fractional probability current density is developed and discussed we also discuss the relationships between the fractional and standard schrodinger equations

the fractional schrodinger equation with hardy type potentials and sign changing nonlinearities abstract we look for solutions to a fractional schrodinger equation of the following form 2 u v x x u f x u k x u q 2 u o n r n 0 where v is bounded and close to periodic potential and x is a hardy type potential we assume that v is positive and f has the subcritical growth but not higher than u q 2 u if is positive and small enough we find a ground state solution i e a critical point of the energy being minimizer on the nehari manifold if is negative we show that there is no ground state solutions we are also interested in an asymptotic behaviour of solutions as 0 and k 0

concentrating standing waves for the fractional nonlinear schrodinger equation abstract we consider the semilinear equation e 2 s s u v x u u p 0 u 0 u h 2 s r n where 0 s 1 1 p n 2 s n 2 s v x is a sufficiently smooth potential with inf r v x 0 and e 0 is a small number letting w be the radial ground state of s w w w p 0 in h 2 s r n we build solutions of the form u e x i 1 k w i x i e e where i v i e and the i e approach suitable critical points of v via a lyapunov schmidt variational reduction we recover various existence results already known for the case s 1 in particular such a solution exists around k nondegenerate critical points of v for s 1 this corresponds to the classical results by floer and weinstein 13 and oh 24 25

on compact complex surfaces of kahler rank one the kahler rank of compact complex surfaces was introduced by harvey and lawson in their 1983 paper on kahler manifolds as a measure of kahlerianity here we give a partial classification of compact complex surfaces of kahler rank 1 these are either elliptic surfaces or hopf surfaces or they admit a holomorphic foliation of a very special type as a consequence we give an affirmative answer to the question raised by harvey and lawson whether the kahler rank is a bimeromorphic invariant

on the compactification of concave ends let x be a complex manifold which admits a proper strictly plurisubharmonic function x a b where a b it is well known that the hausdorffness of h1 x is necessary for the existence of a stein completion of x we show that this condition is also sufficient

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

consensus conditions for general second order multi agent systems with communication delay this paper studies the consensus problem for a class of general second order multi agent systems mass with communication delay we first consider the delay free case and obtain a necessary and sufficient condition for consensus then based on the obtained conditions for the delay free case we deduce an explicit formula for the delay margin of the consensus for the case with time delay using the relationship between the roots of the characteristic equation and the time delay parameter in addition we consider the special case where the second order model is a double integrator for this case simpler consensus conditions under communication delay are provided

on a fractional magnetic schrodinger equation in r with exponential critical growth abstract we deal with a class of fractional magnetic schrodinger equations in the whole line with exponential critical growth under a local condition on the potential we use penalization methods and ljusternik schnirelmann category theory to investigate the existence multiplicity and concentration of nontrivial weak solutions

non degeneracy of positive solutions of kirchhoff equations and its application abstract a non degeneracy theorem for positive solutions of the standard kirchhoff model is proved in all cases except for n 5 and b r n q 2 d x 2 n 4 n 4 2 n 2 n 2 2 in particular for dimensions n 5 and b r n q 2 d x 2 n 4 n 4 2 n 2 n 2 2 we show that there exist two non degenerate positive solutions of the kirchhoff equations which seem to be completely different from the result of the standard schrodinger equation the effects of the non local term on the positive solution set are also studied we show that the non local term has no effect on the structure of the positive solution set for dimensions 1 n 3 and the effects eventually appear for dimensions n 4 with the non degeneracy property of positive solutions of the limit problem we construct concentrated solutions of a singularly perturbed kirchhoff problem via the well known lyapunov schmidt reduction method for dimensions n 5 the existence result of concentrated solutions is completely new and is not implied by the main result of g m figueiredo et al in 19 where a generalized singularly perturbed kirchhoff problem was considered

strongly plurisubharmonic exhaustion functions on 1 convex spaces the conclusion obtained from a stein space by blowing up finitely many points means precisely that there exist a compact analytic set s c x with d imxs 0 for any x s a stein space 14 a finite set a c y and a proper holomorphic map p x y inducing a biholomorphism x s y a and which satisfies p c x cr r following a customary terminology x is called an 1 convex space s its exceptional set and y the remmert reduction of x theorem 1 1 was conjectured by fornaess narashimhan in 5 in this paper we prove the converse

consensus of a class of second order multi agent systems with time delay and jointly connected topologies this technical note investigates consensus problems of a class of second order continuous time multi agent systems with time delay and jointly connected topologies we first introduce a neighbor based linear protocol with time delay then we derive a sufficient condition in terms of linear matrix inequalities lmis for average consensus of the system furthermore we discuss the case where the time delay affects only the information that is being transmitted and show that consensus can be reached with arbitrary bounded time delay finally simulation results are provided to demonstrate the effectiveness of our theoretical results

multiplicity and concentration of solutions for a fractional schrodinger equation via nehari method and pseudo index theory we study a nonlinear fractional schrodinger equation motivated by nonlocal quantum mechanics under suitable assumptions on the potentials we explore the existence concentration convergence and decay estimates of ground state solutions for this equation moreover the multiplicity of solutions is constructed via pseudo index theory and the existence of sign changing solutions is obtained via the nehari method we study a nonlinear fractional schrodinger equation motivated by nonlocal quantum mechanics under suitable assumptions on the potentials we explore the existence concentration convergence and decay estimates of ground state solutions for this equation moreover the multiplicity of solutions is constructed via pseudo index theory and the existence of sign changing solutions is obtained via the nehari method

semiclassical analysis for pseudo relativistic hartree equations abstract in this paper we study the semiclassical limit for the pseudo relativistic hartree equation e 2 m 2 u v u i u p u p 2 u in r n where m 0 2 p 2 n n 1 v r n r is an external scalar potential i x c n x n is a convolution kernel c n is a positive constant and n 1 p n n for n 3 p 2 our equation becomes the pseudo relativistic hartree equation with coulomb kernel

positive and sign changing clusters around saddle points of the potential for nonlinear elliptic problems we study the existence and asymptotic behavior of positive and sign changing multipeak solutions for the equation varepsilon 2 delta v v x v f v quad rm in mathbb r n where e is a small positive parameter f a superlinear subcritical and odd nonlinearity v a uniformly positive potential no symmetry on v is assumed it is known kang and wei in adv differ equ 5 899 928 2000 that this equation has positive multipeak solutions with all peaks approaching a local maximum of v it is also proved that solutions alternating positive and negative spikes exist in the case of a minimum see d aprile and pistoia in ann inst h poincare anal non lineaire 26 1423 1451 2009 the aim of this paper is to show the existence of both positive and sign changing multipeak solutions around a nondegenerate saddle point of v

asymptotic behavior of solutions for nonlinear elliptic problems with the fractional laplacian abstract in this paper we study the asymptotic behavior of least energy solutions and the existence of multiple bubbling solutions of nonlinear elliptic equations involving the fractional laplacians and the critical exponents this work can be seen as a nonlocal analog of the results of han 1991 24 and rey 1990 35

delay robustness in consensus problems we investigate the robustness of consensus schemes for linear multi agent systems mas to feedback delays to achieve this we develop a unified framework that considers linear mas models with different feedback delays e g affecting only the neighbor s output or affecting both the agent s own and its neighbors output this framework has the advantage of providing scalable simple and accurate set valued conditions for consensus using these set valued conditions previous results on consensus in mas with delays can be recovered and generalized moreover we use them to derive conditions for the convergence rate of single integrator mas with feedback delays finally building on this framework we propose a scalable delay dependent design algorithm for consensus controllers for a large class of linear mas

an immersion theorem for vaisman manifolds a locally conformally kahler lck manifold is a complex manifold admitting a kahler covering open image in new window with monodromy acting on open image in new window by kahler homotheties a compact lck manifold is vaisman if it admits a holomorphic flow acting by non trivial homotheties on open image in new window we prove that any compact vaisman manifold admits a natural holomorphic immersion to a hopf manifold n 0 as an application we obtain that any sasakian manifold has a contact immersion to an odd dimensional sphere

on higher dimensional singularities for the fractional yamabe problem a nonlocal mazzeo pacard program we consider the problem of constructing solutions to the fractional yamabe problem which are singular at a given smooth submanifold for which we establish the classical gluing method of mazzeo and pacard j differential geom 1996 for the scalar curvature in the fractional setting this proof is based on the analysis of the model linearized operator which amounts to the study of a fractional order ordinary differential equation ode thus our main contribution here is the development of new methods coming from conformal geometry and scattering theory for the study of nonlocal odes note however that no traditional phase plane analysis is available here instead we first provide a rigorous construction of radial fast decaying solutions by a blowup argument and a bifurcation method then second we use conformal geometry to rewrite this nonlocal ode giving a hint of what a nonlocal phase plane analysis should be third for the linear theory we use complex analysis and some non euclidean harmonic analysis to examine a fractional schrodinger equation with a hardy type critical potential we construct its green s function deduce fredholm properties and analyze its asymptotics at the singular points in the spirit of frobenius method surprisingly enough a fractional linear ode may still have a 2 dimensional kernel as in the second order case