existence theorems for the dirichlet problem without growth restrictions x 0 x 1 0 x 0 x 1 0 have virtually identical growth as lx 1 co however the first problem has no solutions while the second one has one solution the essential point here is the location of zeros of polynomials y2 7 and y2 ii actually granas guenther and lee 3 have proved that the problem x g x x 0 x 1 0 has at least one solution if g has two zeros of opposite sign in this paper we shall prove the following result 0 1

on the existence of solutions for a class of fourth order differential equations abstract we study the existence of the homoclinic solution of a class of nonlinear fourth order ordinary differential equations which involve particular cases of the extended fisher kolmogorov and swift hohenberg equations we address the case when the source term possesses a nonlinear dependence on the first order derivative of the solution the main result follows from an iterative method using the sequence of solutions obtained through the mountain pass technique in order to illustrate this method some numerical examples are shown

semilinear elliptic variational inequalities with dependence on the gradient via mountain pass techniques abstract in this paper we consider a semilinear variational inequality with a gradient dependent nonlinear term obviously the nature of this problem is non variational nevertheless we study that problem associating a suitable semilinear variational inequality variational in nature with it and performing an iterative technique used in de figueiredo et al 2004 6 in order to treat semilinear elliptic equations when there is a gradient dependence on the nonlinearity we prove the existence of a non trivial non negative weak solution u for our problem using essentially variational methods a penalization technique and an iterative scheme via lewy stampacchia s estimates and regularity theory for elliptic equation we also show that u is differentiable and its gradient is h lder continuous on for any 0 1

f manifolds with flat structure and dubrovin s duality this work continues the study of f manifolds m first defined in hema int math res notices 6 1999 277 286 preprint math qa 9810132 and investigated in he frobenius manifolds and moduli spaces for singularities cambridge university press cambridge 2002 the notion of a compatible flat structure is introduced and it is shown that many constructions known for frobenius manifolds do not in fact require invariant metrics and can be developed for all such triples m in particular we extend and generalize recent dubrovin s duality du2 on almost duality for frobenius manifolds preprint math dg 0307374

on the regularity of weak solutions of a one dimensional two phase degenerate stefan problem with convection we shall be concerned with the following one dimensional two phase stefan problem let t 0 and q 0 1 x 0 t find a pair of functions u x t s t which are defined on qt and 0 t respectively and which satisfy al u uxx f u u in x t o x s l o t t l la az ub4 u xx in x t s t x l o tdt l lb u s t r 0 o t t l lc i t u s t t u s t t o t t lid u 0 t 1 06t t l le u 1 t 1 obt t l lf u x 0 u x o x l 1 k s 0 so e 0 1 l lh here so is a given number and the ar a f and u are known functions of their arguments problem 1 1 may be viewed as a model of heat conduction in a region involving phase change an example situation is an ice water mix in which circulation of the water is present then the term f u u represents the contribution of the field velocity generated by the water flow in the liquid phase a more detailed discussion on the formulation of 1 1 can be found elsewhere see e g s

prop profile of poisson geometry it is shown that some classical local geometries are of infinity origin i e their smooth formal germs are homotopy representations of cofibrant di operads in spaces concentrated in degree zero in particular they admit natural infinity generalizations when one considers homotopy representations of the di operads in generic differential graded spaces poisson geometry provides us with a simplest manifestation of this phenomenon

infinite hierarchies of nonlocal symmetries of the chen kontsevich schwarz type for the oriented associativity equations we construct infinite hierarchies of nonlocal higher symmetries for the oriented associativity equations using solutions of associated vector and scalar spectral problems the symmetries in question generalize those found by chen kontsevich and schwarz nucl phys b 730 352 63 for the wdvv equations as a byproduct we obtain a darboux type transformation and a conditional backlund transformation for the oriented associativity equations

another look at cesaro sequence spaces abstract we consider the cesaro sequence space ces p as a closed subspace of the infinite l p sum of finite dimensional spaces we easily obtain many known results for example ces p has property of rolewicz uniform opial property and weak uniform normal structure we also consider some generalized cesaro sequence spaces finally we compute the von neumann jordan and james constants of the two dimensional cesaro sequence space ces p 2 when 1 p 2

poisson bracket on 1 forms and evolutionary partial differential equations we introduce a bracket on 1 forms defined on i e the infinite jet extension of the space of loops and prove that it satisfies the standard properties of a poisson bracket using this bracket we show that certain hierarchies appearing in the framework of f manifolds with a compatible flat connection m are hamiltonian in a generalized sense moreover we show that if a metric g compatible with is also invariant with respect to then this generalized hamiltonian setup reduces to the standard one

purely non local hamiltonian formalism kohno connections and systems in this paper we extend purely non local hamiltonian formalism to a class of riemannian f manifolds without assumptions on the semisimplicity of the product or on the flatness of the connection in the flat case we show that the recurrence relations for the principal hierarchy can be re interpreted using a local and purely non local hamiltonian operators and in this case they split into two lenard magri chains one involving the even terms the other involving the odd terms furthermore we give an elementary proof that the kohno property and the system condition are equivalent under suitable assumptions and we show how to associate a purely non local hamiltonian structure to any system including degenerate ones

on a degenerate diffusion equation of the form c z t ϑ zx x with application to population dynamics 51 here l u and v are strictly positive constants m 1 and i c s for 60 for s o 1 2 with c 0 the initial data z0 will always belong to w 3m q and often to c d and will always have zb 0 zo l u and z l v problem i arises in a theory developed in 173 for two interacting biological species that disperse in response to population pressure this theory is based on the assumption that the individual dispersal velocities are proportional to u u with u and v the corresponding densities if we assume that the habitat q is isolated then the resulting initial value problem has

stabilization of solutions of a degenerate nonlinear diffusion problem i 4 u f u in l l x r u tl t o in r u x 0 uo x in l l where m 1 is a parameter f is locally lipschitz continuous f 0 0 and u is bounded problems of this form arise in a number of areas of science for instance in models for gas or fluid flow in porous media 2 and for the spread of certain biological populations 13 161 this paper is divided into two parts in part i we consider what may be called the motivating example problem i which consists of problem i with the special choice f u u 1 u u a 1 for suitably restricted parameters a we begin by describing in detail the set l of nonnegative equilibrium solutions of problem i clearly 8 l contains the trivial solution u 0 for all l 0 write 8 l e l o in the description of z l there are two critical parameter values lo and l1 with 0 lo l1 j we show that i g l 4 for 0 l lo

dubrovin s duality for f manifolds with eventual identities abstract a vector field e on an f manifold m e is an eventual identity if it is invertible and the multiplication x y x y e 1 defines a new f manifold structure on m we give a characterization of such eventual identities this being a problem raised by manin 2005 12 we develop a duality between f manifolds with eventual identities and we show that this duality is compatible with the local irreducible decomposition of f manifolds and preserves the class of riemannian f manifolds we find necessary and sufficient conditions on the eventual identity which ensure that the classes of harmonic higgs bundles d c h k structures and weak cv structures are preserved by our duality examples of such structures are given in the case of a semi simple multiplication we use eventual identities to construct compatible pairs of metrics

logarithmic frobenius structures and coxeter discriminants abstract we consider a class of solutions of the wdvv equation related to the special systems of covectors called systems and show that the corresponding logarithmic frobenius structures can be naturally restricted to any intersection of the corresponding hyperplanes for the coxeter arrangements the corresponding structures are shown to be almost dual in dubrovin s sense to the frobenius structures on the strata in the discriminants discussed by strachan for the classical coxeter root systems this leads to the families of systems from the earlier work by chalykh and veselov for the exceptional coxeter root systems we give the complete list of the corresponding systems we present also some new families of systems which cannot be obtained in such a way from the coxeter root systems

periodic solutions for extended fisher kolmogorov and swift hohenberg equations by truncature techniques abstract combining truncature techniques with a variational approach we establish an existence result for nontrivial periodic solutions for a class of fourth order ordinary differential equations involving extended fisher kolmogorov and swift hohenberg equations

regular flat structure and generalized okubo system we study a relationship between regular flat structures and generalized okubo systems we show that the space of variables of isomonodromic deformations of a regular generalized okubo system can be equipped with a flat structure as its consequence we introduce flat structures on the spaces of independent variables of generic solutions to classical painleve equations except for pi in our framework the painleve equations pvi pii can be treated uniformly as just one system of differential equations called the four dimensional extended wdvv equation then the well known coalescence cascade of the painleve equations corresponds to the degeneration scheme of the jordan normal forms of a square matrix of rank four

topological degree method in functional boundary value problems let x be the banach space of co functions on j o 11 endowed with the sup norm il 11 denote by 9 the set of all operators k x x which are continuous and bounded i e k a is bounded for any bounded s1 c x and the set of all functionals y x r which are linear bounded and increasing i e x y e x x t y t on j y x y y in the paper we consider the second order differential equation

periodic solutions of parabolic elliptic obstacle problems this paper deals with parabolic elliptic obstacle problems the problem is formulated as follows let sz be a bounded domain in rn iv 1 and for each i e r let 9 t be a relatively compact domain in sz for a given interval z to tl cc d to t co we then define non cylindrical subsets qjz i 1 2 of ix sz by

a sub supersolution approach for a quasilinear kirchhoff equation in this paper we establish an existence result for a quasilinear kirchhoff equation via a sub and supersolution approach by using the minty browder s theorem for pseudomonotone operators theory

regularity results for an elliptic parabolic free boundary problem on etudie un probleme aux limites libre elliptique parabolique a une dimension d espace on donne plusieurs resultats de regularite pour la solution faible et la frontiere libre on donne des conditions pour que la frontiere libre soit une courbe c 1

positive and negative solutions of a quasi linear elliptic equation by a mountain pass method and truncature techniques abstract the existence of a positive and a negative solution of a problem of the type u f x u u 0 in u 0 on is proved when f has a growth at infinity depending both on u and on u the techniques are based on an iterative scheme of mountain pass approximated solutions and the use of a suitable truncature method

existence results for quasilinear elliptic exterior problems involving convection term and nonlinear robin boundary conditions abstract in this paper the authors establish the existence of solutions for a class of elliptic exterior problems involving convection terms and nonlinear robin boundary conditions the proof of the result is made by combining galerkin method with a priori estimates for this kind of problem

existence and nonexistence of solutions for quasilinear elliptic equations abstract in this paper we study the problem p u f x u u in u 0 on where r n is a smooth bounded domain n 2 and p u div u p 2 u defines the p laplacian we provide some necessary and sufficient conditions on f under which the problem admits a weak solution for the case p 2 we obtain more general conditions on f the main ingredients are degree theory and the super subsolution method

regularizing effects for ut aϑ u 0 in l1 abstract various initial boundary value problems and cauchy problems can be written in the form du dt a u 0 where r r is nondecreasing and a is the linear generator of strongly continuous nonexpansive semigroup e ta in an l1 space for example if a subject perhaps to suitable boundary conditions we obtain equations arising in flow in a porous medium or plasma physics depending on the choice of while if a x acting in l1 r we have a scalar conservation law in this paper we show that if m m 0 and m 2 m 2 where 1 1 then roughly speaking the norm of t du dt may be estimated in terms of the initial data u0 in l1 such estimates give information about the regularity of solutions asymptotic behaviour etc in applications side issues such as the introduction of sufficiently regular approximate problems on which estimates can be made and the assignment of a precise meaning to the operator a are also dealt with these considerations are of independent interest

convergence of a finite volume scheme for a system of interacting species with cross diffusion in this work we present the convergence of a positivity preserving semi discrete finite volume scheme for a coupled system of two non local partial differential equations with cross diffusion the key to proving the convergence result is to establish positivity in order to obtain a discrete energy estimate to obtain compactness we numerically observe the convergence to reference solutions with a first order accuracy in space moreover we recover segregated stationary states in spite of the regularising effect of the self diffusion however if the self diffusion or the cross diffusion is strong enough mixing occurs while both densities remain continuous