on the solvability of periodic boundary value problems with impulse in this work we obtain some new results concerning the existence of solutions to an impulsive first order nonlinear ordinary differential equation with periodic boundary conditions the ideas involve differential inequalities and schaefer s fixed point theorem

correction to cartan subalgebras of simple lie algebras trans amer math soc 234 1977 no 2 435 446 mr0480650 58 806

homoclinic solutions for a class of subquadratic second order hamiltonian systems in this paper we study the existence of infinitely many homoclinic solutions for a class of subquadratic second order hamiltonian systems by using the variant fountain theorem we obtain a new criterion for guaranteeing that second order hamiltonian systems has infinitely many homoclinic solutions recent results from the literature are generalized and significantly improved an example is also given in this paper to illustrate our main results

infinitely many solutions for a class of nonlinear impulsive differential equations with periodic boundary conditions in this paper we consider the existence of solutions for a class of nonlinear impulsive problems with periodic boundary conditions by using critical point theory we obtain some existence theorems of infinitely many solutions for the nonlinear impulsive problem when the impulsive functions are superlinear we extend and improve some recent results

simple lie algebras of small characteristic vi completion of the classification let l be a finite dimensional simple lie algebra over an algebraically closed field of characteristic p 3 it is proved in this paper that if the p envelope of adl in derl contains a torus of maximal dimension whose centralizer in adl acts nontriangulably on l then p 5 and l is isomorphic to one of the melikian algebras m m n in conjunction with a premet h strade simple lie algebras of small characteristic v the non melikian case j algebra 314 2007 664 692 theorem 1 2 this implies that up to isomorphism any finite dimensional simple lie algebra over an algebraically closed field of characteristic p 3 is either classical or a filtered lie algebra of cartan type or a melikian algebra of characteristic 5 this result finally settles the classification problem for finite dimensional simple lie algebras over algebraically closed fields of characteristic 2 3

existence and multiplicity of solutions for second order impulsive differential equations with dirichlet problems abstract in this paper we consider the existence and the multiplicity of solutions for second order impulsive differential equations with dirichlet boundary conditions some new existence results are obtained by critical point theory our results further improve some existing results

simple lie algebras of small characteristic iv solvable and classical roots abstract let l be a finite dimensional simple lie algebra over an algebraically closed field f of characteristic p 3 and t a torus of maximal dimension in the p envelope of l in der l in this paper we describe the t semisimple quotients of the 2 sections of l relative to t and prove that if all 1 sections of l relative to t are compositionally classical or solvable then l is either classical or a block algebra or a filtered lie algebra of type s

existence and multiplicity of solutions for some dirichlet problems with impulsive effects abstract in this paper we consider the existence and multiplicity of solutions for some dirichlet impulsive problems and some existence and multiplicity results are obtained the solutions are sought by means of lax milgram theorem and some critical theorems

simple lie algebras of small characteristic v the non melikian case abstract let l be a finite dimensional simple lie algebra over an algebraically closed field f of characteristic p 3 we prove in this paper that if for every torus t of maximal dimension in the p envelope of adl in derl the centralizer of t in adl acts triangulably on l then l is either classical or of cartan type as a consequence we obtain that any finite dimensional simple lie algebra over an algebraically closed field of characteristic p 5 is either classical or of cartan type this settles the last remaining case of the generalized kostrikin shafarevich conjecture the case where p 7

existence of solutions for some fourth order boundary value problems with parameters abstract in this paper existence and multiplicity results for solutions are obtained for the fourth order boundary value problem bvp u 4 t u t u t f t u t 0 t 1 u 0 u 1 u 0 u 1 0 where f 0 1 r r is continuous r and r are parameters by using the critical point theory and morse theory we obtain that if satisfy 4 2 1 then the above bvp has solutions where is in some different intervals

boundary value problems for a class of impulsive functional equations this paper is related to the existence and approximation of solutions for impulsive functional differential equations with periodic boundary conditions we study the existence and approximation of extremal solutions to different types of functional differential equations with impulses at fixed times by the use of the monotone method some of the options included in this formulation are differential equations with maximum and integro differential equations in this paper we also prove that the lipschitzian character of the function which introduces the functional dependence in a differential equation is not a necessary condition for the development of the monotone iterative technique to obtain a solution and to approximate the extremal solutions to the equation in a given functional interval the corresponding results are established for the impulsive case the general formulation includes several types of functional dependence delay equations equations with maxima integro differential equations finally we consider the case of functional dependence which is given by nonincreasing and bounded functions

existence for a semilinear sixth order ode abstract in this paper we study the existence and multiplicity of nontrivial solutions for a boundary value problem associated with a semilinear sixth order ordinary differential equation arising in the study of spatial patterns our treatment is based on variational tools including two brezis nirenberg s linking theorems

existence and multiplicity of solutions for fourth order boundary value problems with parameters abstract in this paper we study the existence and multiplicity of the solutions for the fourth order boundary value problem bvp u 4 t u t u t f t u t 0 t 1 u 0 u 1 u 0 u 1 0 where f 0 1 r r is continuous r and r are parameters by means of the idea of the decomposition of operators shown by chen w y chen a decomposition problem for operators xuebao of dongbei renmin university 1 1957 95 98 see also m krasnosel skii topological methods in the theory of nonlinear integral equations gostehizdat moscow 1956 and the critical point theory we obtain that if the pair is on the curve 2 4 satisfying 2 2 then the above bvp has at least one two three and infinitely many solutions for being in different interval respectively

existence of solutions to a class of nonlinear second order two point boundary value problems in this paper the existence and multiplicity results of solutions are obtained for the second order two point boundary value problem u t f t u t for all t 0 1 subject to u 0 u 1 0 where f is continuous the monotone operator theory and critical point theory are employed to discuss this problem respectively in argument quadratic root operator and its properties play an important role

nonlinear boundary value problem of first order impulsive functional differential equations this paper discusses nonlinear boundary value problem for first order impulsive functional differential equations we establish several existence results by using the lower and upper solutions and monotone iterative techniques two examples are discussed to illustrate the efficiency of the obtained results

three solutions for a p laplacian boundary value problem with impulsive effects in this paper a p laplacian boundary value problem with impulsive effects is considered multiplicity of solutions is obtained by three critical points theorem an example is presented to illustrate main result

periodic solutions for ordinary differential equations with sublinear impulsive effects abstract the continuation method of topological degree is used to investigate the existence of periodic solutions for ordinary differential equations with sublinear impulsive effects the applications of the abstract approach include the generalizations of some classical nonresonance theorem for impulsive equations for instance the existence theorem for asymptotically positively homogeneous differential systems and the existence theorem for second order equations with landesman lazer conditions

classification of the restricted simple lie algebras soit l une algebre de lie simple restreinte de dimension finie sur un corps algebriquement clos f de caracteristique p 7 alors l est de type classique ou de cartan

a boundary value problem for fourth order elastic beam equations multiplicity results for a fourth order nonlinear boundary value problem are presented the proof of the main result is based on the critical point theory

simple lie algebras of small characteristic i sandwich elements abstract let l be a finite dimensional simple lie algebra over an algebraically closed field of characteristic p 3 of absolute toral rank 2 and t a 2 dimensional torus in the semisimple p envelope of l it is proved that l is either classical or a block algebra or contains sandwich elements which are homogeneous with respect to t or a conjugate to t in addition several dimension estimates are given

wavelet multiple correlation and cross correlation a multiscale analysis of eurozone stock markets abstract statistical studies that consider multiscale relationships among several variables use wavelet correlations and cross correlations between pairs of variables this procedure needs to calculate and compare a large number of wavelet statistics the analysis can then be rather confusing and even frustrating since it may fail to indicate clearly the multiscale overall relationship that might exist among the variables this paper presents two new statistical tools that help to determine the overall correlation for the whole multivariate set on a scale by scale basis this is illustrated in the analysis of a multivariate set of daily eurozone stock market returns during a recent period wavelet multiple correlation analysis reveals the existence of a nearly exact linear relationship for periods longer than the year which can be interpreted as perfect integration of these euro stock markets at the longest time scales it also shows that small inconsistencies between euro markets seem to be just short within year discrepancies possibly due to the interaction of different agents with different trading horizons

periodic solution generated by impulses for singular differential equations abstract in this paper we study the existence of a positive periodic solution for second order singular differential equations with impulsive conditions the proof is based on the mountain pass theorem we show that this positive periodic solution is generated by impulses

tori in the melikian algebra this paper is concerned with the tori in the restricted melikian algebra g g 1 1 according to the latest classification result of premet and strade 16 g is the unique simple lie algebra of toral rank 2 over an algebraically closed field of characteristic p 5 distinct from the classical algebras and algebras of cartan type here we determine the one dimensional subtori in g up to conjugation by automorphisms and compute their centralizers in g one consequence of this investigation is that all maximal tori in g are two dimensional for each two dimensional torus we find the number of its roots of any possible type classical witt hamiltonian proper the answer depends only on the position of the torus relative to the invariant filtration of g the conjugacy classes of two dimensional tori are not determined in this paper it can be shown that their number is infinite the classification of simple lie algebras requires detailed information about the toral structure of low rank lie algebras see e g 3 19 one of the key points is the possibility of finding a torus of maximal dimension in the p envelope of a simple lie algebra l having all roots proper the classical argument is based on checking that when switching an improper root to a proper one the number of proper roots in every 2 section of l increases in the case of the melikian algebra we encounter a situation when the number of proper roots remains unchanged when this does occur we show that the number of hamiltonian roots becomes strictly less

the classification of the simple modular lie algebras ii the toral structure abstract let l be a simple lie algebra over an algebraically closed field of characteristic p 7 and t an optimal torus in some p envelope l p we determine the action of t on the two sections of l which have been described in st4 we also give some new and noncomputational proofs to determine the conjugacy classes of the tori in w n 1 and of the cartan subalgebras of w 1 n

periodic solutions of non autonomous second order hamiltonian systems the purpose of this paper is to study the existence of periodic solutions for a class of non autonomous second order hamiltonian system some new existence theorems are obtained by the least action principle

an application of variational method to second order impulsive differential equation on the half line abstract in this paper we study the multiplicity of solutions for second order impulsive differential equation with a parameter on the half line by using a variational method and a three critical points theorem we give some new criteria to guarantee that the impulsive problem has at least three classical solutions also an example is given in this paper to illustrate the main results

new comparison results for impulsive integro differential equations and applications we prove some new maximum principles for ordinary integro differential equations this allows us to introduce a new definition of lower and upper solutions which leads to the development of the monotone iterative technique for a periodic boundary value problem related to a nonlinear first order impulsive integro differential equation

the existence and multiplicity of solutions for an impulsive differential equation with two parameters via a variational method abstract in this paper we study the existence and multiplicity of classical solutions for a second order impulsive differential equation with periodic boundary conditions by using a variational method and critical point theory we give some new criteria to guarantee that the impulsive problem has at least one solution two solutions and infinitely many solutions when the parameter pair c lies in different intervals respectively some examples are given in this paper to illustrate the main results

impulsive periodic boundary value problems of first order differential equations in this paper by using schaeffer s theorem we prove new existence theorems for a nonlinear periodic boundary value problem of first order differential equations with impulses our results improve and generalize some known results

the classification of the simple modular lie algebras iii solution of the classical case we investigate the structure of simple modular lie algebras over an algebraically closed field of characteristic p 7 if the distinguished subalgebra q l t with respect to an optimal torus t in some p envelope lp of l equals l then either l has a two section of type h 2 1 z or l is of classical type