q convergence of nets and weak separation axioms in fuzzy lattices abstract in this paper we introduce the concept of q remote neighborhood and establish the q convergence theory of nets in fuzzy lattices next we introduce the st i i 1 0 1 2 separation axioms in fuzzy lattices and discuss some of their characterizations finally we introduce and study s irresolute order homomorphism and s homeomorphism discuss the application of q convergence of nets and show that the st i i 1 0 1 2 separability is preserved under s homeomorphism

fuzzy non continuous mappings and fuzzy pre semi separation axioms the aim of the paper is mainly to introduce and study fuzzy pre semi open mapping fuzzy pre semi irresolute mapping fuzzy pre semi separation axioms and fuzzy pre semi connectedness in fuzzy topological spaces

on a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients we develop a perturbation theory for stochastic differential equations sdes by which we mean both stochastic ordinary differential equations sodes and stochastic partial differential equations spdes in particular we estimate the l p distance between the solution process of an sde and an arbitrary ito process which we view as a perturbation of the solution process of the sde by the l q distances of the differences of the local characteristics for suitable p q 0 as one application of the developed perturbation theory we establish strong convergence rates for numerical approximations of a class of sodes with nonglobally monotone coefficients as another application of the developed perturbation theory we prove strong convergence rates for spatial spectral galerkin approximations of solutions of semilinear spdes with nonglobally monotone nonlinearities including cahn hilliard cook type equations and stochastic burgers equations further applications of the developed perturbation theory include regularity analyses of solutions of sdes with respect to their initial values as well as small noise analyses for ordinary and partial differential equations

existence of solutions and boundary asymptotic behavior of p r laplacian equation multi point boundary value problems abstract this paper investigates the problem p r u r f r u 0 r 0 r u 0 i 1 m i u i e 0 u r as r r where p r u u p r 2 u is called the p r laplacian r is a singular coefficient the existence and nonexistence of solutions are discussed and the exact boundary blow up rate of solutions is given

asymptotic behavior of large solution to elliptic equation of bieberbach rademacher type with convection terms we analyze the asymptotic behavior of solutions to nonlinear elliptic equation du u q b x f u in w subject to the singular boundary condition u x as dist x email protected 0 where w is a smooth bounded domain in r n email protected email protected rv r r 0 for some email protected c 2 a lim u l u and l nrv 1 our approach employs karamata regular variation theory combined with the method of lower and supper solution

ps convergence theory of fuzzy nets and its applications the convergence theory not only is an significantly basic theory of fuzzy topology and fuzzy analysis but also has wide applications in fuzzy inference and some other aspects in this paper we introduce the concept of psc remote neighborhood of fuzzy points and establish the moore smith ps convergence theory of fuzzy nets also we discuss the applications of ps convergence of fuzzy nets

absolute continuity and numerical approximation of stochastic cahn hilliard equation with unbounded noise diffusion abstract in this article we consider the absolute continuity and numerical approximation of the solution of the stochastic cahn hilliard equation with unbounded noise diffusion we first obtain the holder continuity and malliavin differentiability of the solution of the stochastic cahn hilliard equation by using the strong convergence of the spectral gakerkin approximation then we prove the existence and strict positivity of the density function of the law of the exact solution for the stochastic cahn hilliard equation with sublinear growth diffusion coefficient which fills a gap for the existed result when the diffusion coefficient satisfies a growth condition of order 1 3 1 to approximate the density function of the exact solution we propose a full discretization based on the spatial spectral galerkin approximation and the temporal drift implicit euler scheme furthermore a general framework for deriving the strong convergence rate of the full discretization is developed based on the variation approach and the factorization method consequently we obtain the sharp mean square convergence rates in both time and space via sobolev interpolation inequalities and semigroup theories to the best of our knowledge this is the first result on the convergence rate of full discretizations for the considered equation

nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints hamiltoniens sousquadratiques conditions aux limites infinies et donnees d explosion hamiltoniens superquadratiques formulation viscosite des conditions aux limites le probleme ergodique commande stochastique optimale avec contraintes d etat

asymptotic behavior of large solution for boundary blowup problems with non linear gradient terms let email protected r n n 3 be a bounded domain with smooth boundary we show the asymptotic behavior of boundary blowup solutions to non linear elliptic equation du u q b x f u in w subject to the singular boundary condition u x as dist x email protected 0 f is c varying at our analysis is based on the karamata regular variation theory combined with the method of lower and supper solution

malliavin calculus for the stochastic cahn hilliard allen cahn equation with unbounded noise diffusion abstract the stochastic partial differential equation analyzed in this work is motivated by a simplified mesoscopic physical model for phase separation it describes pattern formation due to adsorption and desorption mechanisms involved in surface processes in the presence of a stochastic driving force this equation is a combination of cahn hilliard and allen cahn type operators with a multiplicative white space time noise of unbounded diffusion we apply malliavin calculus in order to investigate the existence of a density for the stochastic solution u in dimension one according to the regularity result in 5 u admits continuous paths a s using this property and inspired by a method proposed in 8 we construct a modified approximating sequence for u which properly treats the new second order allen cahn operator under a localization argument we prove that the malliavin derivative of u exists locally and that the law of u is absolutely continuous establishing thus that a density exists

existence and boundary blow up rates of solutions for boundary blow up elliptic systems abstract in this paper we study some elliptic systems with boundary blow up conditions in a smooth bounded domain by constructing the suitable upper and lower solutions we discuss the existence and global estimate of the positive solution furthermore the boundary blow up rates of the positive solution are also partly discussed

full discretization of semilinear stochastic wave equations driven by multiplicative noise a fully discrete approximation of the semilinear stochastic wave equation driven by multiplicative noise is presented a standard linear finite element approximation is used in space and a stochastic trigonometric method is used for the temporal approximation this explicit time integrator allows for mean square error bounds independent of the space discretization and thus does not suffer from a step size restriction as in the often used stormer verlet leapfrog scheme furthermore it satisfies an almost trace formula i e a linear drift of the expected value of the energy of the problem numerical experiments are presented and confirm the theoretical results

net theoretical convergence in l m fuzzy cotopological spaces in this paper we introduce the notion of topological l m fuzzy convergence structure and prove that for a given set there exists a bijection between the set of all topological l m fuzzy convergence structures and the set of all l m fuzzy cotopologies on this set this induces an isomorphism between the category of topological l m fuzzy convergence spaces and the category of l m fuzzy cotopological spaces

boundary blow up in nonlinear elliptic equations of bieberbach rademacher type the research of the first author was carried out at victoria university melbourne with the support of the australian government through detya the second author has been supported by grant 2 cex06 11 18 2006

large solution to nonlinear elliptic equation with nonlinear gradient terms abstract the aim of this paper is to study the qualitative behavior of large solutions to the following problem u a x u q b x f u x u x x here a x c is a positive function with 0 1 b x c is a non negative function and may be singular near the boundary or vanish on the boundary and the nonlinear term f is a varying function whose variation at infinity is not regular we focus our investigation on the existence and asymptotic behavior close to the boundary of large solutions by karamata regular variation theory and the method of upper and lower solution the main results of this paper emphasize the central role played by the gradient term u q and the weight functions a x and b x

finite element approximation of the cahn hilliard cook equation we study the nonlinear stochastic cahn hilliard equation perturbed by additive colored noise we show almost sure existence and regularity of solutions we introduce spatial approximation by a standard finite element method and prove error estimates of optimal order on sets of probability arbitrarily close to 1 we also prove strong convergence without known rate

a trigonometric method for the linear stochastic wave equation a fully discrete approximation of the linear stochastic wave equation driven by additive noise is presented a standard finite element method is used for the spatial discretization and a stochastic trigonometric scheme for the temporal approximation this explicit time integrator allows for error bounds independent of the space discretization and thus does not have a step size restriction as in the often used stormer verlet leap frog scheme moreover it enjoys a trace formula as does the exact solution of our problem these favorable properties are demonstrated with numerical experiments

on ground state solutions for singular and semi linear problems including super linear terms at infinity abstract we establish a result concerning the existence of entire positive classical and bounded solutions which converge to zero at infinity for the semi linear equation u f x u x r n where f r n 0 0 is a suitable function and 0 is a real parameter this result completes the principal theorem of a mohammed a mohammed ground state solutions for singular semi linear elliptic equations nonlinear analysis 2008 doi 10 1016 j na 2008 11 080 mainly because his result does not address the super linear terms at infinity penalty arguments lower upper solutions and an approximation procedure will be used

nonlinear aspects of the cahn hilliard equation abstract this paper treats phase separation within the context of the phenomenological cahn hilliard equation c t m c f c k 2 c where c is the concentration m c is the mobility and f c is homogeneou s free energy which is assumed here to be a fourth degree polynomial natural boundary conditions are introduced the full set of equilibrium solutions is specified a comparison theorem for stability criteria which was postulated by langer is proved here within the framework of the natural boundary conditions energy methods are used to define and estimate the limit of monotonic global stability it is pointed out that within the parameter region where the uniform homogeneous state is the only equilibrium solution there may still exist some internal excitable region in which the homogeneous solution possesses growing fluctuations furthermore a periodic instability is shown to exist in the metastable region in addition to the well known nucleation instability

strong and weak convergence rates of a spatial approximation for stochastic partial differential equation with one sided lipschitz coefficient strong and weak approximation errors of a spatial finite element method are analyzed for the stochastic partial differential equations spdes with one sided lipschitz coefficients including the s

the asymptotic behaviour of solutions with boundary blow up for semilinear elliptic equations with nonlinear gradient terms abstract in this paper we show existence uniqueness and exact asymptotic behaviour of solutions near the boundary to nonlinear elliptic problems u u q k x g u x u where is a bounded domain with smooth boundary in r n 0 q 0 2 lim d x 0 k x d x c 0 0 2 c 0 0 g c 1 0 g 0 0 g is increasing on 0 and is karamata regular variation function at infinity with index 1 and 0

strong convergence rate of finite difference approximations for stochastic cubic schrodinger equations abstract in this paper we derive a strong convergence rate of spatial finite difference approximations for both focusing and defocusing stochastic cubic schrodinger equations driven by a multiplicative q wiener process beyond the uniform boundedness of moments for high order derivatives of the exact solution the key requirement of our approach is the exponential integrability of both the exact and numerical solutions by constructing and analyzing a lyapunov functional and its discrete correspondence we derive the uniform boundedness of moments for high order derivatives of the exact solution and the first order derivative of the numerical solution which immediately yields the well posedness of both the continuous and discrete problems the latter exponential integrability is obtained through a variant of a criterion given by cox hutzenthaler and jentzen arxiv 1309 5595 as a by product of this exponential integrability we prove that the exact and numerical solutions depend continuously on the initial data and obtain a large deviation type result on the dependence of the noise with first order strong convergence rate

the hamiltonian structure of the maxwell vlasov equations morrison 25 has observed that the maxwell vlasov and poisson vlasov equations for a collisionless plasma can be written in hamiltonian form relative to a certain poisson bracket we derive another poisson structure for these equations by using general methods of symplectic geometry the main ingredients in our construction are the symplectic structure on the co adjoint orbits for the group of canonical transformations and the symplectic structure for the phase space of the electromagnetic field regarded as a gauge theory our poisson bracket satisfies the jacobi identity whereas morrison s does not 37 our construction also shows where canonical variables can be found and can be applied to the yang mills vlasov equations and to electromagnetic fluid dynamics

keller osserman type conditions for some elliptic problems with gradient terms in this paper we consider the elliptic boundary blow up problems u g u f u in u on where is a smooth bounded domain and the functions f and g are increasing and continuous our main concern will be to prove both existence and nonexistence of nonnegative solutions depending on new integral conditions of keller osserman type involving f and g we show in particular that the problem with a minus sign may have solutions inclusive for some functions g with slightly superquadratic growth at infinity that is somehow not expected we also obtain uniqueness of nonnegative solutions in some cases

fuzzy preopen sets and fuzzy preseparation axioms abstract in this paper the concept of preopen sets due to a s mashhour m e abd el monsef and s n el debb 7 has been generalised to the fuzzy setting further fuzzy separation axioms have been introduced and investigated with the help of fuzzy preopen sets

strong convergence of a fully discrete finite element approximation of the stochastic cahn hilliard equation we consider the stochastic cahn hilliard equation driven by additive gaussian noise in a convex domain with polygonal boundary in dimension d le 3 we discretize the equation using a standard fi

strong convergence rate of splitting schemes for stochastic nonlinear schrodinger equations abstract in this paper we show that solutions of stochastic nonlinear schrodinger nls equations can be approximated by solutions of coupled splitting systems based on these systems we propose a new kind of fully discrete splitting schemes which possess algebraic strong convergence rates for stochastic nls equations key ingredients of our approach are using the exponential integrability and stability of the corresponding splitting systems and numerical approximations in particular under very mild conditions we derive the optimal strong convergence rate o n 2 1 2 of the spectral splitting crank nicolson scheme where n and denote the dimension of the approximate space and the time step size respectively

theory of topological molecular lattices abstract the aim of this paper is to bring the theories of point set topology fuzzy topology and l fuzzy topology into a unified theory the theory of topological molecular lattices for this purpose we first introduce the concepts of molecule for completely distributive complete lattice molecular lattice for short the cotopology on it and the concept of remote neighborhoods of molecules therefrom we develop the theory of pointwise topology on molecular lattices

a necessary and sufficient condition for existence of large solutions to semilinear elliptic equations we consider the semilinear equation u p x f u on a domain rn n 3 where f is a nonnegative nondecreasing continuous function which vanishes at the origin and p is a nonnegative continuous function with the property that any zero of p is contained in a bounded domain in such that p is positive on its boundary for bounded we show that a nonnegative solution u satisfying u x as x exists if and only if the function s s0 f t dt satisfies 1 s 1 2 ds for unbounded including rn we show that a similar result holds where u x as x within and u x as x if p x decays to zero rapidly as x

nondegeneracy and uniqueness for boundary blow up elliptic problems abstract in this paper we use for the first time linearization techniques to deal with boundary blow up elliptic problems after introducing a convenient functional setting we show that the problem u a x u p g x u in with u on has a unique positive solution for large enough and determine its asymptotic behavior as here p 1 a x is a continuous function which can be singular near and g x u is a perturbation term with potential growth near zero and infinity we also consider more general problems obtained by replacing u p by e u or a logistic type function f u

preservation of physical properties of stochastic maxwell equations with additive noise via stochastic multi symplectic methods stochastic maxwell equations with additive noise are a system of stochastic hamiltonian partial differential equations intrinsically possessing the stochastic multi symplectic conservation law it is shown that the averaged energy increases linearly with respect to the evolution of time and the flow of stochastic maxwell equations with additive noise preserves the divergence in the sense of expectation moreover we propose three novel stochastic multi symplectic methods to discretize stochastic maxwell equations in order to investigate the preservation of these properties numerically we make theoretical discussions and comparisons on all of the three methods to observe that all of them preserve the corresponding discrete version of the averaged divergence meanwhile we obtain the corresponding dissipative property of the discrete averaged energy satisfied by each method especially the evolution rates of the averaged energies for all of the three methods are derived which are in accordance with the continuous case numerical experiments are performed to verify our theoretical results

a stochastic multi symplectic scheme for stochastic maxwell equations with additive noise abstract in this paper we investigate a stochastic multi symplectic method for stochastic maxwell equations with additive noise based on the stochastic version of variational principle we find a way to obtain the stochastic multi symplectic structure of three dimensional 3 d stochastic maxwell equations with additive noise we propose a stochastic multi symplectic scheme and show that it preserves the stochastic multi symplectic conservation law and the local and global stochastic energy dissipative properties which the equations themselves possess numerical experiments are performed to verify the numerical behaviors of the stochastic multi symplectic scheme

analysis of a splitting scheme for damped stochastic nonlinear schrodinger equation with multiplicative noise in this paper we investigate the damped stochastic nonlinear schrodinger nls equation with multiplicative noise and its splitting based approximation when the damped effect is large enough we

exponential integrators for stochastic maxwell s equations driven by ito noise abstract this article presents explicit exponential integrators for stochastic maxwell s equations driven by both multiplicative and additive noises by utilizing the regularity estimate of the mild solution we first prove that the strong order of the numerical approximation is 1 2 for general multiplicative noise combining a proper decomposition with the stochastic fubini s theorem the strong order of the proposed scheme is shown to be 1 for additive noise moreover for linear stochastic maxwell s equation with additive noise the proposed time integrator is shown to preserve exactly the symplectic structure the evolution of the energy as well as the evolution of the divergence in the sense of expectation several numerical experiments are presented in order to verify our theoretical findings

boundary behavior of large solutions to semilinear elliptic equations with nonlinear gradient terms abstract in this paper we study the boundary behavior of solutions to boundary blow up elliptic problems u u q b x f u x u where is a bounded domain with smooth boundary in r n q 0 b c which is positive in and may be vanishing on the boundary and rapidly varying near the boundary and f is rapidly varying or normalized regularly varying at infinity

boundary blow up elliptic problems of bieberbach and rademacher type with nonlinear gradient terms abstract by a perturbation method and constructing comparison functions we show the exact asymptotic behaviour of solutions near the boundary to nonlinear elliptic problems u u q b x e u x u where is a bounded domain with smooth boundary in r n q 0 b is non negative and non trivial in which may be vanishing on the boundary

boundary blow up quasilinear elliptic problems of the bieberbach type with nonlinear gradient terms abstract by a perturbation method and by constructing comparison functions we show the exact asymptotic behaviour of solutions near the boundary of the quasilinear elliptic problem div u m 2 u u x q m 1 b x e u x x u where is a c 2 bounded domain with a smooth boundary in r n n 2 m 1 q 0 b is nonnegative and nontrivial in which may vanish on the boundary

the asymptotic behaviour of solutions with blow up at the boundary for semilinear elliptic problems abstract by constructing the comparison functions and the perturbed method it is showed that any solution u c 2 to the semilinear elliptic problems u k x g u x u satisfies lim d x 0 u x z d x 2 2 2 c 0 2 1 where is a bounded domain with smooth boundary in r n lim d x 0 k x d x c 0 2 c 0 0 2 2 g c 1 0 g 0 and g s s is increasing on 0 there exists 0 such that lim s g s g s 0 z s d t 2 g t s g t 0 t g s d s

fuzzy strongly semiopen sets and fuzzy strong semicontinuity abstract in this paper we first introduce and study the fuzzy strongly semiopen and fuzzy strongly semiclosed sets in fuzzy space then we introduce the strong semi interior and strong semiclosure of a fuzzy set and kuratowski s 14 sets theorem of general topology is generalized finally we introduce the fuzzy strongly semicontinuous fuzzy strongly semiopen and fuzzy strongly semiclosed mappings on fuzzy topological spaces and also establish some of their characteristic properties and discuss relations between fuzzy continuous fuzzy semicontinuous and fuzzy strongly semicontinuous mappings

existence and regularity of solution for a stochastic cahn hilliard allen cahn equation with unbounded noise diffusion the cahn hilliard allen cahn equation with noise is a simplified mean field model of stochastic microscopic dynamics associated with adsorption and desorption spin flip mechanisms in the context of surface processes for such an equation we consider a multiplicative space time white noise with diffusion coefficient of sub linear growth using technics from semigroup theory we prove existence and path regularity of stochastic solution depending on that of the initial condition our results are also valid for the stochastic cahn hilliard equation with unbounded noise diffusion for which previous results were established only in the framework of a bounded diffusion coefficient we prove that the path regularity of stochastic solution depends on that of the initial condition and are identical to those proved for the stochastic cahn hilliard equation and a bounded noise diffusion coefficient if the initial condition vanishes they are strictly less than 2 d 2 in space and 1 2 d 8 in time as expected from the theory of parabolic operators in the sense of petrovski the bi laplacian operator seems to be dominant in the combined model

nonlinear elliptic equations with singular boundary conditions abstract we consider the model problem formula where is a bounded region in r n with smooth boundary q 0 2 and k u u p p 1 or e u we show that there exists a classical solution

on the boundary blow up solutions of p x laplacian equations with singular coefficient abstract this paper investigates the problem p x u x f x u 0 in u x as d x 0 where p x u div u p x 2 u is called the p x laplacian x is a singular coefficient the existence and nonexistence of boundary blow up solutions are discussed and the singularity of the boundary blow up solution is given