mild solutions of non autonomous second order problems with nonlocal initial conditions abstract in this paper we establish the existence of mild solutions for a non autonomous abstract semi linear second order differential equation submitted to nonlocal initial conditions our approach relies on the existence of an evolution operator for the corresponding linear equation and the properties of the hausdorff measure of non compactness

fekete points and convergence towards equilibrium measures on complex manifolds building on bb1 we prove a general criterion for convergence of possibly singular bergman measures towards pluripotential theoretic equilibrium measures on complex manifolds the criterion may be formulated in terms of the growth properties of the unit balls of certain norms on holomorphic sections or equivalently as an asymptotic minimization property for generalized donaldson l functionals our result settles in particular a well known conjecture in pluripotential theory concerning the equidistribution of fekete points and it gives the convergence of bergman measures towards the equilibrium measure for bernstein markov measures applications to interpolation of holomorphic sections are also discussed

global attractor for a class of functional differential inclusions with hille yosida operators abstract we study the dynamics for a class of functional differential inclusions whose linear part generates an integrated semigroup some techniques of measure of noncompactness are deployed to prove the global solvability and the existence of a compact global attractor for the m semiflow generated by our system the obtained results generalize recent ones in the same direction

the stability of solutions to the complex monge ampere equations in bounded f hyperconvex domains abstract in this paper we study the complex monge ampere equations in bounded f hyperconvex domains we will prove a stability result for solutions

weak convergence of currents we give certain condictions to guarantee weak convergence u kt k rightarrow ut where u k u are plurisubharmonic functions and t k t are positive closed currents as applications we obtain that convergence in capacity of plurisubharmonic functions u k implies weak convergence of the complex monge amp ere measures dd cu k n if all of the plurisubharmonic functions u k are bounded below by one of some sorts of plurisubharmonic functions

kahler einstein metrics and the kahler ricci flow on log fano varieties we prove the existence and uniqueness of kahler einstein metrics on q fano varieties with log terminal singularities and more generally on log fano pairs whose mabuchi functional is proper we study analogues of the works of perelman on the convergence of the normalized kahler ricci flow and of keller rubinstein on its discrete version ricci iteration in the special case of non singular fano manifolds our results on ricci iteration yield smooth convergence without any additional condition improving on previous results our result for the kahler ricci flow provides weak convergence independently of perelman s celebrated estimates

monge ampere equations in big cohomology classes we define non pluripolar products of an arbitrary number of closed positive 1 1 currents on a compact kahler manifold x given a big 1 1 cohomology class on x i e a class that can be represented by a strictly positive current and a positive measure on x of total mass equal to the volume of and putting no mass on pluripolar sets we show that can be written in a unique way as the top degree self intersection in the non pluripolar sense of a closed positive current in we then extend kolodziedj s approach to sup norm estimates to show that the solution has minimal singularities in the sense of demailly if has l 1 e density with respect to lebesgue measure if is smooth and positive everywhere we prove that t is smooth on the ample locus of provided is nef using a fixed point theorem we finally explain how to construct singular kahler einstein volume forms with minimal singularities on varieties of general type

periodic solutions for a class of differential inclusions in general banach spaces abstract let x be a real banach space a d a x x an m accretive operator and f r d a x a multi function which is 2 periodic with respect to its first argument has nonempty closed convex and weakly compact values and is strongly weakly upper semicontinuous in this paper we prove the existence of at least one solution for the problem u t a u t f t f t f t u t u t u t 2 in the case in which f satisfies an appropriate sign condition

maximality of plurifinely plurisubharmonic functions abstract in this paper we introduce and study a subclass m of the class of f plurisubharmonic functions in an f open set our main result shows that f maximality is an f local notion for negative functions from m

growth of balls of holomorphic sections and energy at equilibrium let l be a big line bundle on a compact complex manifold x given a non pluripolar compact subset k of x and a continuous hermitian metric e on l we define the energy at equilibrium of k as the monge ampere energy of the extremal psh weight associated to k we prove the differentiability of the energy at equilibrium with respect to and we show that this energy describes the asymptotic behaviour as k of the volume of the sup norm unit ball induced by k k on the space of global holomorphic sections h 0 x kl as a consequence of these results we recover and extend rumely s robin type formula for the transfinite diameter we also obtain an asymptotic description of the analytic torsion and extend yuan s equidistribution theorem for algebraic points of small height to the case of a big line bundle

existence in the large for nonlinear delay evolution inclusions with nonlocal initial conditions in this paper we provide a sufficient condition for the existence of c0 solutions for a class of nonlinear functional differential evolution equation of the form u t au t f t t r f t f t u t ut t r u t g u t t 0 where x is a real banach space a is the infinitesimal generator of a nonlinear compact semigroup f r x c 0 d a x is a nonempty convex and weakly compact valued multi function and g cb d a c 0 d a

a class of nonlinear evolution equations subjected to nonlocal initial conditions abstract we prove the existence of c 0 solutions for a class of nonlinear evolution equations subjected to nonlocal initial conditions of the form u t a u t f t f t f t u t u 0 g u where a d a x x is an m accretive operator acting on the infinite dimensional banach space x f 0 2 d a x is an almost strongly weakly u s c multi function which satisfies an appropriate sign condition while g c 0 2 d a d a is a continuous function

existence and uniqueness of periodic solution for a class of semilinear evolution equations this paper deals with the existence and uniqueness for the periodic boundary value problem of the semilinear evolution equation in a hilbert space h u t au t f t u t 0 t u 0 u where a d a h h is a positive definite self adjoint operator 0 and f 0 h h satisfy caratheodory condition we present some spectral conditions for the nonlinearity f t u to guarantee the existence and uniqueness these spectral conditions are the generalization for nonresonance condition of the self adjoint elliptic boundary value problems

existence results and asymptotic behavior for nonlocal abstract cauchy problems the purpose of this paper is to study the existence and asymptotic behavior of solutions for cauchy problems with nonlocal initial datum generated by accretive operators in banach spaces

a comparison principle for the complex monge ampere operator in cegrell s classes and applications in this article we will first prove a result about the convergence in capacity next we will obtain a general decomposition theorem for complex monge ampere measures which will be used to prove a c

continuity of the complex monge ampere operator on compact kahler manifolds we prove several approximation theorems of the complex monge ampere operator on a compact kahler manifold as an application we prove the cegrell type theorem on a complete description of the range of the complex monge ampere operator in the class of plurisubharmonic functions with vanishing complex monge ampere mass on all pluripolar sets as a by product we obtain a stability theorem of solutions of complex monge ampere equations

fine topology silov boundary and ddc n on considere la topologie fine des fonctions plurisousharmoniques on etablit des theoremes de convergence on etudie les definitions de dd c n l operateur dd c n converge pour des limites monotones des fonctions plurisousharmoniques bornees

distribution of rational maps with a preperiodic critical point let f lambda be a family of rational maps of a fixed degree with a marked critical point c lambda under a natural assumption we first prove that the hypersurfaces of parameters for which c lambda is periodic converge as a sequence of positive closed 1 1 currents to the bifurcation current attached to c and defined by demarco we then turn our attention to the parameter space of polynomials of a fixed degree d by intersecting the d 1 currents attached to each critical point of a polynomial bassaneli and berteloot obtained a positive measure mu rm bif of finite mass which is supported on the connectedness locus they showed that its support is included in the closure of the set of parameters admitting d 1 neutral cycles we show that the support of this measure is precisely the closure of the set of strictly critically finite polynomials i e of misiurewicz points

weighted pluripotential theory in cn let k c n be compact and let w be a nonnegative uppersemicontinuous function on k with z k w z 0 nonpluripolar let q log w and define the weighted pluricomplex green function v

the weighted monge ampere energy of quasiplurisubharmonic functions abstract we study degenerate complex monge ampere equations on a compact kahler manifold x we show that the complex monge ampere operator d d c n is well defined on the class e x of plurisubharmonic functions with finite weighted monge ampere energy the class e x is the largest class of psh functions on which the monge ampere operator is well defined and the comparison principle is valid it contains several functions whose gradient is not square integrable we give a complete description of the range of the operator d d c n on e x as well as on some of its subclasses we also study uniqueness properties extending calabi s result to this unbounded and degenerate situation and we give applications to complex dynamics and to the existence of singular kahler einstein metrics

existence and asymptotic stability of periodic solution for evolution equations with delays abstract in this paper we discuss the existence and asymptotic stability of the time periodic solution for the evolution equation with multiple delays in a hilbert space h u t a u t f t u t u t 1 u t n t r where a d a h h is a positive definite selfadjoint operator f r h n 1 h is a nonlinear mapping which is periodic in t and 1 2 n are positive constants we present essential conditions on the nonlinearity f to guarantee that the equation has periodic solutions or an asymptotically stable periodic solution the discussion is based on analytic semigroups theory and an integral inequality with delays

goodness of fit testing for time series models via distance covariance abstract in many statistical modeling frameworks goodness of fit tests are typically administered to the estimated residuals in the time series setting whiteness of the residuals is assessed using the sample autocorrelation function for many time series models especially those used for financial time series the key assumption on the residuals is that they are in fact independent and not just uncorrelated in this paper we apply the auto distance covariance function adcv to evaluate the serial dependence of the estimated residuals distance covariance can discriminate between dependence and independence of two random vectors the limit behavior of the test statistic based on the adcv is derived for a general class of time series models one of the key aspects in this theory is adjusting for the dependence that arises due to parameter estimation this adjustment has essentially the same form regardless of the model specification we illustrate the results in simulated examples

dynamics of rational maps lyapunov exponents bifurcations and capacity let l f log df d f denote the lyapunov exponent of a rational map f p 1 p 1 in this paper we show that for any holomorphic family of rational maps f x of degree d 1 t f dd c l f defines a natural positive 1 1 current on x supported exactly on the bifurcation locus of the family the proof is based on the following potential theoretic formula for the lyapunov exponent here f c 2 c 2 is a homogeneous polynomial lift of f g f is the escape rate function of f and capk f is the homogeneous capacity of the filled julia set of f we show in particular that the capacity of k f is given explicitly by the formula where res f is the resultant of the polynomial coordinate functions of f we introduce the homogeneous capacity of compact circled and pseudoconvex sets k c 2 and show that the levi measure determined by the geometry of k is the unique equilibrium measure such k c 2 correspond to metrics of non negative curvature on p 1 and we obtain a variational characterization of curvature

the mabuchi geometry of finite energy classes abstract we introduce different finsler metrics on the space of smooth kahler potentials that will induce a natural geometry on various finite energy classes e x motivated by questions raised by r berman v guedj and y rubinstein we characterize the underlying topology of these spaces in terms of convergence in energy and give applications of our results to existence of kahler einstein metrics on fano manifolds

stability and regularity of solutions of the monge ampere equation on hermitian manifolds abstract we prove stability of solutions of the complex monge ampere equation on compact hermitian manifolds when the right hand side varies in a bounded set in l p p 1 and it is bounded away from zero such solutions are shown to be holder continuous as an application we extend a recent result of szekelyhidi and tosatti on kahler einstein equation from kahler to hermitian manifolds

nonlinear evolution inclusions topological characterizations of solution sets and applications this paper deals with a nonlinear delay differential inclusion of evolution type involving m dissipative operator and source term of multi valued type in a banach space under rather mild conditions the r structure of c0 solution set is studied on compact intervals which is then used to obtain the r property on non compact intervals secondly the result about the structure is furthermore employed to show the existence of c0 solutions for the inclusion mentioned above subject to nonlocal condition defined on right half line no nonexpansive condition on nonlocal function is needed as samples of applications we consider a partial differential inclusion with time delay and then with nonlocal condition at the end of the paper

picard and weakly picard operators technique for nonlinear differential equations in banach spaces abstract in this paper we study nonlocal cauchy problems for differential equations in banach spaces using picard and weakly picard operators technique and suitable bielecki norms some existence uniqueness and data dependence results are obtained under some mild conditions as an application we also discuss a class of impulsive cauchy problems by adapting the same methods

periodic solutions of nonlinear evolution inclusions abstract in this paper we establish the existence of periodic trajectories for a class of nonlinear time varying evolution inclusions in which the multivalued term is nonconvex valued an example of a parabolic system is also presented in detail

plurisubharmonic and holomorphic functions relative to the plurifine topology a weak and a strong concept of plurifinely plurisubharmonic and plurifinely holomorphic functions are introduced strong will imply weak the weak concept is studied further a function f is weakly plurifinely plurisubharmonic if and only if it is locally bounded from above in the plurifine topology and f h is finely subharmonic for all complex affine linear maps h as a consequence the regularization in the plurifine topology of a pointwise supremum of such functions is weakly plurifinely plurisubharmonic and it differs from the pointwise supremum at most on a pluripolar set weak plurifine plurisubharmonicity and weak plurifine holomorphy are preserved under composition with weakly plurifinely holomorphic maps

monge ampere measures associated to extremal plurisubharmonic functions in ⁿ we consider the extremal plurisubharmonic functions le and ue associated to a nonpluripolar compact subset e of the unit ball b c c and show that the corresponding monge ampere measures dd l and dd ue are mutually absolutely continuous we then discuss the polynomial growth condition l a generalization of leja s polynomial condition in the plane and study the relationship between the asymptotic behavior of the orthogonal polynomials associated to a measure on e and the l condition

approximation of plurifinely plurisubharmonic functions abstract in this study we consider the approximation of a negative plurifinely plurisubharmonic function defined on a plurifinely domain by an increasing sequence of plurisubharmonic functions defined in euclidean domains

an equality on the complex monge ampere measures abstract in this study we extend an equality on the complex monge ampere measures of bedford taylor which holds in the class of locally bounded plurisubharmonic functions to the class e introduced and investigated by cegrell in 4 and the class of plurisubharmonic functions that are bounded near the boundary

density and intersection of 1 1 currents abstract we study density currents associated with a collection of positive closed 1 1 currents on a complex manifold we prove that the density current is unique and determined by the usual wedge product in some classical situations including the case where the currents have bounded potentials as an application we compare density currents with the non pluripolar product and the andersson wulcan product we also analyse some situations where the wedge product is not well defined but the density can be explicitly computed

non autonomous evolution inclusions with nonlocal history conditions global integral solutions abstract this paper is concerned with nonlinear nonlocal differential inclusion of evolution type in frechet spaces defined on right half line the underlying feature of the inclusion under consideration is that it is non autonomous we obtain some compactness characterizations of integral solution sets for the inclusion without nonlinear perturbations then making use of these characterizations we derive a new existence result of global integral solutions for the original inclusion no invariance condition on the nonlinearity is involved the results we obtained here extend the semilinear case of the previous related ones such as i i vrabie existence in the large for nonlinear delay evolution inclusions with nonlocal initial conditions j funct anal 262 2012 1363 1391 and are new even for the case of the nonlinearity being a single valued function

existence for nonlinear evolution inclusions with nonlocal retarded initial conditions abstract in this paper we prove a sufficient condition for the global existence of bounded c 0 solutions for a class of nonlinear functional differential evolution equation of the form u t a u t f t t 0 f t f t u t u t 1 u t n t 0 u t g u t t 0 where x is a real banach space a is the infinitesimal generator of a nonlinear compact semigroup f r d a n 1 x is a nonempty convex weakly compact valued and almost strongly weakly u s c multi function and g c b d a c 0 d a is nonexpansive

existence for reaction diffusion systems a compactness method approach the authors study the existence of weak solutions for the following system ut u f u v vt v g u v in 0 t u v 0 on 0 t u 0 x u0 x v 0 x v0 x in the region rn with smooth boundary the functions r r are assumed to be continuous and nondecreasing with 0 0 0 u0 v0 l f g r2 2r with f an upper semicontinuous mapping u s c the following local existence results are shown 1 for the diffusive case i e when both and are strictly increasing with u s c g 2 for the semi diffusive case only one function is strictly increasing with g being either with separated variables i e having the form of the product or of the sum of two functions g u and h v or globally lipschitz with respect to its second variable i e g u v g u v l v v for each u b r v v r and some l l b additional conditions of linear form on the growth of f and g are indicated to guarantee global existence results