ternary 2n point lagrange subdivision schemes ternary 2n point lagrange subdivision schemes with a tension parameter are analyzed it is shown that the resulting curves are c 3 c 4 and c 5 continuous for the values of n 2 3 and 4 respectively the role of the tension parameter in subdivision scheme is demonstrated by a few examples

construction of binary four and five point non stationary subdivision schemes from hyperbolic b splines binary non stationary four and five point subdivision schemes have been developed using hyperbolic b spline basis functions the proposed subdivision schemes generate pleasing curves near the control polygon as compared to the existing non stationary subdivision schemes developed using trigonometric b splines basis functions the main speciality of the hyperbolic subdivision schemes is that they can regenerate hyperbolas and parabolas quite efficiently

multiplicity results for some elliptic systems near resonance with a nonprincipal eigenvalue abstract some multiplicity results of solutions are obtained for a class of elliptic systems which are near resonance with a nonprincipal eigenvalue by the classical saddle point theorem and a local saddle point theorem in critical point theory

generation of fractal curves and surfaces using ternary 4 point interpolatory subdivision scheme in this paper the generation of fractal curves and surfaces along with their properties using ternary 4 point interpolatory subdivision scheme with one parameter are analyzed the relationship between the tension parameter and the fractal behavior of the limiting curve is demonstrated through different examples the specific range of the tension parameter has also been depicted which provides a clear way to generate fractal curves since the fractal scheme introduces in the paper have more number of control points therefore it gives more degree of freedom to control the shape of the fractal curve

existence of three nontrivial solutions for a class of superlinear elliptic equations abstract the existence of three nontrivial solutions for a class of superlinear elliptic equations is obtained by using variational theorems of mixed type due to marino and saccon and linking theorem

numerical grid generation in arbitrary surfaces through a second order differential geometric model abstract in this paper a set of second order partial differential equations for the generation of coordinates in a given surface has been developed and then solved numerically to demonstrate its potential for surface coordinate generation the proposed equations are not some arbitrarily chosen equations but are a consequence of the formulae of gauss and thus carry with them an explicit dependence on the geometric properties of the given surface furthermore these equations are easy to solve and require only the specification of the bounding curves to provide the dirichlet boundary conditions for their solution results of coordinate generation both in simply and doubly connected regions on some known surfaces with the option of coordinate redistribution have been presented extension of this technique to arbitrary surfaces seems to be straightforward

fractal behavior of ternary 4 point interpolatory subdivision scheme with tension parameter in this paper the fractal curves and surfaces of ternary 4 point interpolatory subdivision scheme are developed and analyzed the fractal range of the tension parameter has also been determined the behavior of fractal curves and surfaces corresponding to different values of parameter has been depicted through six examples which offers direct means for an effective generation of subdivision fractals the real life applications of the proposed fractal subdivision scheme has also been demonstrated

on a new notion of linking and application to elliptic problems at resonance abstract in this paper we introduce a new notion of linking which includes in particular the notions of homotopical linking and local linking critical point theorems for continuous functionals on metric spaces are presented finally an application to nonlinear elliptic problems at resonance is given

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

hyperbolic forms of ternary non stationary subdivision schemes originated from hyperbolic b splines in this work ternary non stationary subdivision schemes based on hyperbolic b spline basis functions have been presented the proposed hyperbolic ternary three point and four point subdivision schemes give pleasing as well as consistent curves with the control polygons as compared to the existing non stationary subdivision schemes obtained from trigonometric b splines the main speciality of the hyperbolic schemes is that they can reproduce hyperbolas and parabolas quite efficiently which has been demonstrated with the help of curvature plots

existence and multiplicity of solutions for asymptotically linear noncooperative elliptic systems abstract using the minimax methods in critical point theory and a generalized landesman lazer type condition we establish two existence results of solutions for asymptotically linear noncooperative elliptic systems at resonance besides this we obtain two solutions in the case of near resonance

fractal interpolation surfaces derived from fractal interpolation functions based on the construction of fractal interpolation functions a new construction of fractal interpolation surfaces on arbitrary data is presented and some interesting properties of them are proved finally a lower bound of their box counting dimension is provided

a non stationary binary three point approximating subdivision scheme in this paper we present a non stationary binary three point approximating subdivision scheme which can generate a wide variety of c3 continuous limit curves with different initial control parameter 0 the continuity of the scheme is proved by using the conclusion in dyn and levin 1995 5 the advantage of the scheme is illustrated by a number of examples

multiplicity of solutions for a class of fourth elliptic equations we show that there exist at least three nontrivial solutions for a class of fourth elliptic equations under navier boundary conditions by linking approaches

multiple solutions of semilinear elliptic problems in a ball in this paper lower bounds for the number of solutions of semilinear elliptic problems in a ball of rn are given its hypotheses are only related to the behavior of the nonlinearities at and at 0 global assumptions are never made for example oddness is never required for the proof of multiplicity results

a combined ternary 4 point subdivision scheme combined binary 6 point interpolating and approximating subdivision scheme with tension parameters is analyzed it is shown that the resulting curves are c1 c2 interpolating continuous and c1 c2 c3 approximating continuous for different values of tension parameters the role of the tension parameters in subdivision scheme are illustrated using a few examples

exact multiplicity for some quasilinear elliptic dirichlet problems where the non linearity changes sign abstract the exact multiplicity of positive solutions is obtained for a class of quasilinear elliptic dirichlet problems where the non linearity changes sign meanwhile the uniqueness of positive ground state on r n is also obtained

resonance problems for the p laplacian systems abstract two existence theorems of the solutions are obtained for the p laplacian systems at resonance under a landesman lazer type condition by critical point theory

some existence theorems for elliptic resonant problems some existence theorems are obtained for the elliptic resonant problems at either the first eigenvalue or the higher eigenvalues with unbounded nonlinearity by using the minimax methods in critical point theory

bifurcation from infinity and multiple solutions for some discrete sturm liouville problems in this paper we study nonlinear discrete boundary value problems of the form d p t 1 dy t 1 q t y t l email protected y t f t y t h t email protected t a 1 1y a a 1 email protected a 0 a 2 1y b 1 a 2 email protected b 1 0 where l k is an eigenvalue of the associated linear problem l is a parameter and f satisfies the sublinear growth condition f t s a s a b email protected a 1 b 1 email protected r for some email protected email protected 1 and a email protected 0 we study the existence and multiplicity of solutions for the above mentioned problems by establishing some a priori bounds together with leray schauder continuation and bifurcation arguments

fractal properties of the generalized chaikin corner cutting subdivision scheme in this paper we analyze the fractal properties of the generalized chaikin corner cutting subdivision scheme with two arbitrary parameters on the basis of the discussion of limit points on the limit curve the fractal range of the scheme is obtained and illustrated the results obtained suggest a clear direction for generating fractal curves by using this scheme two fractal examples and their complexity evaluation results obtained by using the box dimension are given

binary 3 point and 4 point non stationary subdivision schemes using hyperbolic function in this paper binary 3 point and 4 point non stationary subdivision schemes are presented using hyperbolic function as basis function asymptotic equivalence method is used to investigate the continuity of the proposed schemes comparison between the proposed schemes their stationary counterparts and some existing non stationary schemes has been depicted through examples it can be observed that the proposed schemes have the capability to reproduce conics particularly parabola

fixed point theory and nonlinear problems introduction among the most original and far reaching of the contributions made by henri poincare to mathematics was his introduction of the use of topological or qualitative methods in the study of nonlinear problems in analysis his starting point was the study of the differential equations of celestial mechanics and in particular of their periodic solutions his work on this topic began with his thesis in 1879 and was developed in detail in his great three volume work methodes nouvelles de la mechanique celeste which appeared in the early 1890s and summarized his many memoirs of the intervening period it continued until his memoir shortly before his death in 1912 in which he put forward the unproved fixed point result usually referred to as poincare s last geometric theorem the ideas introduced by poincare include the use of fixed point theorems the continuation method and the general concept of global analysis the writer s acquaintance with poincare s influence came through contact with solomon lefschetz and marston morse both of whom were very explicit as to the role of poincare as an initiator in this direction of mathematical development in 1934 in the foreword to his colloquium volume on the calculus of variations in the large morse had put this forward very forcefully in the first paragraph

on superquadratic elliptic systems in this article we study the existence of solutions for the elliptic system updelta u frac partial h partial v left u v x right text in upomega updelta v frac partial h partial v left u v x right text in upomega u 0 v 0 text on partial upomega where upomega is a bounded open subset of mathbb r n with smooth boundary partial upomega and the function h mathbb r 2 times overline upomega to mathbb r is of class c 1

improved binary four point subdivision scheme and new corner cutting scheme a binary 4 point approximating subdivision scheme presented by siddiqi and ahmad 2006 9 has been improved by introducing a global tension parameter an improved form of the scheme generates a family of c n n 1 2 3 4 limiting curves for certain range of global tension parameter and a c 5 limiting curve for a fixed value also a new corner cutting subdivision scheme has been proposed which generates a limiting curve of c 1 continuity the laurent polynomial method has been used to investigate the order of the derivative continuity of both subdivision schemes the performance of the subdivision schemes has been exposed by considering examples and compared with the existing schemes

a combined approximating and interpolating ternary 4 point subdivision scheme abstract in this paper a new combined approximating and interpolating ternary 4 point subdivision scheme with multiple parameters is proposed a set of nice properties such as support continuity and polynomial generation are briefly discussed the new combined scheme not only contains a lot of classical ternary schemes as special cases but also generates brand new ternary schemes compared to other approximating subdivision schemes limit curves generated by the new scheme are more consistent with the corresponding control polygons and keep detail features better examples are given to show the effectiveness of the scheme furthermore fractal property is analyzed and fractal curves are also given

multiplicity results for a superlinear elliptic system with partial interference with the spectrum abstract in this work we consider an elliptic system of two equations in dimension greater than one with nonlinearities which are linear at and superlinear at we prove by variational techniques which involve a strongly indefinite functional the existence of two solutions for suitable forcing terms under a condition on the linear part which prevents resonance with the eigenvalues of the operator

multiple solutions for an elliptic system near resonance abstract we consider an elliptic system with linear part depending on two parameters and a sublinear perturbation we obtain the existence of at least two solutions when the linear part is near resonance the system is associated with a strongly indefinite functional and the solutions are obtained through saddle point theorem and galerkin approximation

elliptic grid generation conclusions some modi cations for the restriction and prolongation process of multigrid methods have been presented that are necessary for the simulation of complex supersonic ow elds damping of the restricted residual error and blending between a second order central and a rst order upwind prolongation enable convergence in supersonic ows and resulted in strong reductions in cpu time the advantageof this kind of blending is the reduction to rst order prolongationat shock waves only

topological degree for s mappings with maximal monotone perturbations and its applications to variational inequalities abstract this paper is concerned with the topological degree for mappings of class s with maximal monotone perturbations several results and remarks concerning the evaluation of this degree are given in particular it is shown that the local degree for the generalized gradient of nonsmooth functional at the local minimizer is equal to one as applications two examples of elliptic variational inequalities are given where the multiple existence of solutions is discussed

a new non stationary binary 6 point subdivision scheme in this paper the hyperbolic form of binary 6 point interpolating non stationary subdivision scheme has been constructed using the hyperbolic function some of the important properties of the proposed scheme has been discussed the comparison of the proposed scheme with the trigonometric form of binary 6 point interpolatory non stationary scheme is depicted through examples which indicate that the proposed scheme not only accommodates and is more consistent with the control polygon but also generates pleasing curves corresponding to the larger parametric values in and outside the parametric interval as compared to the trigonometric form of binary 6 point scheme developed by daniel et al comparison with some other interpolating non stationary subdivision schemes has also been demonstrated

multiple solutions for semilinear elliptic equations near resonance at higher eigenvalues abstract using the minimax methods in critical point theory and a generalized landesman lazer type condition we obtain two solutions for a class of semilinear elliptic equations near resonance at higher eigenvalues

analysis of asymptotically equivalent binary subdivision schemes non stationary uniform subdivision schemes are presented including some important examples as the up function and exponential splines the multivariate analysis of subdivision schemes is extended to a class of non stationary schemes which are asymptotically equivalent to converging stationary or non stationary schemes

solvability for two point boundary value problems abstract suppose that h l 1 0 g c r r and lim t g t t 0 with the saddle point theorem the solvability is proved for the two point boundary value problemproblem formula under the condition that formula where formula and formula

a variational approach to subquadratic perturbations of elliptic systems abstract we consider subquadratic perturbations of semilinear elliptic systems which are in variational form a unified approach to both the cooperative and noncooperative problems is presented and a condition of nonquadraticity at infinity is introduced to treat the resonant cases through minimax techniques

multiple solutions for a class of nonlinear boundary value problems near resonance a variational approach abstract a variational approach is given to the existence of multiple solutions for some nonlinear boundary value problems near resonance at the first eigenvalue

semilinear elliptic problems near resonance with a nonprincipal eigenvalue abstract we consider the dirichlet problem for the equation u u f x u h x in a bounded domain where f has a sublinear growth and h l 2 we find suitable conditions on f and h in order to have at least two solutions for near to an eigenvalue of a typical example to which our results apply is when f x u behaves at infinity like a x u q 2 u with m a x 0 and 1 q 2

existence and multiplicity results for some elliptic systems at resonance abstract the existence and multiplicity of weak solutions for some resonant elliptic systems are obtained by using ekeland s variational principle the mountain pass theorem and the saddle point theorem in critical point theory

a ternary 4 point approximating subdivision scheme in the implementation of subdivision scheme three of the most important issues are smoothness size of support and approximation order our objective is to introduce an improved ternary 4 point approximating subdivision scheme derived from cubic polynomial interpolation which has smaller support and higher smoothness comparing to binary 4 point and 6 point schemes ternary 3 point and 4 point schemes see table 2 the method is easily generalized to ternary 2n 2 point approximating subdivision schemes we choose a ternary scheme because a way to get smaller support is to raise arity and we use polynomial reproduction to get higher approximation order easily 2007 elsevier inc all rights reserved

bound state nodal solutions for the non autonomous schrodinger poisson system in r3 abstract in general the existence of nodal solution for schrodinger poisson systems with the nonlinearity f x u p 2 u 4 p 6 in r 3 can be established by using the nodal nehari manifold method however for the case where 2 p 4 such an approach is not applicable because palais smale sequences restricted on the nodal nehari manifold can be not bounded in this paper we introduce a novel constraint method to prove the existence of nodal solution to a class of non autonomous schrodinger poisson systems in the case where 2 p 4 we conclude that such solution changes sign exactly once in r 3 and is bounded in h 1 r 3 d 1 2 r 3 moreover the existence of least energy nodal solution is obtained in the case where 1 73 3 p 4 which remains unsolved in the existing literature

smooth curve interpolation with generalized conics abstract efficient algorithms for shape preserving approximation to curves and surfaces are very important in shape design and modelling in cad cam systems in this paper a local algorithm using piecewise generalized conic segments is proposed for shape preserving curve interpolation it is proved that there exists a smooth piecewise generalized conic curve which not only interpolates the data points but also preserves the convexity of the data furthermore if the data is strictly convex then the interpolant could be a locally adjustable gc 2 curve provided the curvatures at the data points are well determined it is also shown that the best approximation order is o h 6 an efficient algorithm for the simultaneous computation of points on the curve is derived so that the curve can be easily computed and displayed the numerical complexity of the algorithm for computing n points on the curve is about 2 n multiplications and n additions finally some numerical examples with graphs are provided and comparisons with both quadratic and cubic spline interpolants are also given

an existence result for a linear superlinear elliptic system with neumann boundary conditions abstract in this work we consider an elliptic system of two equations in dimension one with neumann boundary conditions where the nonlinearities are asymptotically linear at and superlinear at we obtain that under suitable hypotheses a solution exists for any couple of forcing terms in l 2 we also present a similar result in which the superlinearity is in only one of the two equations and we discuss the resonant problem too

existence of solutions for quasilinear elliptic equations abstract using variational methods we study the existence and multiplicity of solutions of the dirichlet problem for the equation div a u p u p 2 u f x u

on a stable family of four point nonlinear subdivision schemes eliminating the gibbs phenomenon abstract the chaikin s scheme presents the interesting property of not producing gibbs phenomenon the problem arises when we need a scheme that provides a higher order of approximation in this case linear schemes are not a good option as they produce gibbs phenomenon close to discontinuities in this article a new four point nonlinear family of subdivision schemes that eliminate the gibbs phenomenon is presented it is based on the linear family of four point subdivision schemes depending on a tension parameter introduced in dyn et al 2005 a simple algebraic transformation leads to an easy way of introducing nonlinearity in the original family of schemes the non interpolatory characteristic of the nonlinear scheme can be modulated just varying the value of the tension parameter results about the stability convergence and the elimination of the gibbs phenomenon are presented some numerical comparisons of the results obtained in the generation of curves are also shown leading to the conclusion that the high order nonlinear schemes are more suitable for this purpose

on interpolatory subdivision from approximating subdivision scheme this paper deals with some theoretical analysis of one strategy for deducing interpolatory from approximating subdivision scheme first we derive the explicit formula for one class of interpolatory subdivision schemes deduced from approximating subdivision schemes this explicit formula paves a way for systematic analysis of interpolatory subdivisions derived by the strategy we analyze the polynomial generation property of interpolatory subdivision derived by the strategy moreover the explicit formula also has the merit of providing a method for designing new interpolatory and approximating subdivisions and some new subdivision schemes are constructed

proving convexity preserving properties of interpolatory subdivision schemes through reconstruction operators we introduce a new approach towards proving convexity preserving properties for interpolatory subdivision schemes our approach is based on the relation between subdivision schemes and prediction operators within harten s framework for multiresolution and hinges on certain convexity properties of the reconstruction operator associated to prediction our results allow us to recover certain known results 10 8 1 7 in addition we are able to determine the necessary conditions for convexity preservation of the family of subdivision schemes based on the hermite interpolation considered in 4

fractal generation using ternary 5 point interpolatory subdivision scheme this paper is devoted to explore the generation of fractal curves and surfaces using ternary 5 point interpolatory subdivision scheme the fractal behavior of the limiting curves and surfaces is analyzed with the help of tension parameter it may be noted that the proposed fractal scheme determines two intervals of range of shape control parameter the behavior of the shape control parameter for the generation of fractals has been visualized through five examples which provides faster rate of generation of fractals

variation and minkowski dimension of fractal interpolation surface the fractal interpolation surface on the rectangular domain is discussed in this paper we study the properties of the oscillation and the variation of bivariate continuous functions then we discuss the special properties of bivariate fractal interpolation function and estimate the value of its variation using the relation between the minkowski dimension of the graph of continuous function and its variation we obtain the exact value of the minkowski dimension of the fractal interpolation surface

elliptic grid generation based on laplace equations and algebraic transformations abstract an elliptic grid generation method is presented to generate boundary conforming grids in domains in 2d and 3d physical space and on minimal surfaces and parametrized surfaces in 3d physical space the elliptic grid generation method is based on the use of a composite mapping this composite mapping consists of a nonlinear transfinite algebraic transformation and an elliptic transformation the elliptic transformation is based on the laplace equations for domains or on the laplace beltrami equations for surfaces the algebraic transformation maps the computational space one to one onto a parameter space the elliptic transformation maps the parameter space one to one onto the domains or surfaces the composition of these two mappings is a differentiable one to one mapping from computational space onto the domains or surfaces and has a nonvanishing jacobian this composite mapping defines the grid point distribution in the interior of the domains or surfaces for domains and minimal surfaces the composite mapping obeys a nonlinear elliptic poisson system with control functions completely defined by the algebraic transformation the solution of the poisson systems is obtained by picard iteration and black box multigrid solvers for parametrized curved surfaces it is not necessary to define and solve a nonlinear elliptic poisson system instead a linear elliptic system and an inversion problem is solved to generate the grid in the interior of the surface

strong resonance for some quasilinear elliptic equations abstract we study the existence of the weak solutions of the nonlinear boundary value problem p u 1 u p 2 u g u h x in u 0 on where the nonlinearity g is of the landesman lazer type our sufficient conditions generalize all previously published results about the strong resonance at the first eigenvalue

existence of nontrivial solutions of semilinear elliptic equations soit cr n un domaine borne a frontiere lisse et g r r une application continue telle que g 0 0 on etudie l existence des solutions non triviales du probleme aux valeurs limites de la forme u g u dans u 0

partial differential equations involving subcritical critical and supercritical nonlinearities abstract we establish the existence of at least one nonnegative solution for the problem p div a u u f u in u 0 on where a and f satisfy conditions near zero here the novelty is that we do not need restrictions on the nonlinearities at infinity therefore we can consider subcritical critical and supercritical cases

landesman lazer type results for second order hamilton jacobi bellman equations we study the boundary value problem f d2u du u x u f x u in u 0on where the second order differential operator f is of hamilton jacobi bellman type f is sub linear in u at infinity and rn is a regular bounded domain we extend the well known landesman lazer conditions to study various bifurcation phenomena taking place near the two principal eigenvalues associated to the differential operator we provide conditions under which the solution branches extend globally along the eigenvalue gap we also present examples illustrating the results and hypotheses

differential systems with strongly indefinite variational structure abstract the euler lagrange equations of lagrangians with a strongly indefinite quadratic part are studied by means of the direct min max method of benci and rabinowitz the simplest case is a system of two coupled semilinear poisson equations using an analytic framework of a suitable family of products of fractional sobolev spaces existence results are obtained for all nonlinearities with subcritical growth rates

multiple solutions for neumann and periodic problems with singular ϕ laplacian abstract we use the critical point theory for convex lower semicontinuous perturbations of c 1 functionals to establish existence of multiple radial solutions for some one parameter neumann problems involving the operator v div v 1 v 2 similar results for periodic problems are also provided