positive solutions for a class of multiparameter ordinary elliptic systems abstract using a fixed point theorem due to m a krasnosel skii the upper lower solutions method and fixed point index theory we study existence non existence and multiplicity of positive solutions for a class of systems of second order ordinary differential equations we give a new notion of superlinearity for nonlinearities observe that the nonlinearities may even be in some sense singular as an application we show multiplicity results for a class of semilinear elliptic systems in both bounded annular domains and exterior domains in addition we apply our results to fourth order boundary value problems

positive solutions for higher order multi point boundary value problems with nonhomogeneous boundary conditions abstract we study nth order boundary value problems with a nonlinear term f t x subject to nonhomogeneous multi point boundary conditions criteria for the existence of positive solutions of such problems are established conditions are determined by the relationship between the behavior of f t x x near 0 and when compared with the smallest positive characteristic value of an associated linear integral operator this work improves and extends some recent results in the literature for the second order problems the results are illustrated with examples

robust stability for multiple model adaptive control part ii gain bounds the axiomatic development of a wide class of estimation based multiple model switched adaptive control emmsac algorithms considered in the first part of this two part contribution forms the basis for the proof of the gain bounds given in this paper the bounds are determined in terms of a cover of the uncertainty set and in particular in many instances are independent of the number of candidate plant models under consideration the full interpretation implications and usage of these bounds within design synthesis are discussed in part i here in part ii key features of the bounds are also discussed and a simulation example is considered it is shown that a dynamic emmsac design can be universal and hence non conservative and hence outperforms static emmsac and other conservative designs a wide range of possible dynamic algorithms are outlined motivated by both performance and implementation considerations

emden fowler equations involving critical exponents on considere le probleme y t k y 2 y 2k 3 0 t 0 pour t 2 0 0 soit t inf t 0 y 0 sur t alors t 0 0 on etudie comment la position t du premier zero de y t varie avec

existence of positive solutions for a system of generalized lidstone problems in this paper we study the existence of positive solutions for the system of generalized lidstone problems for ordinary differential equations 1 mu 2 m f 1 t u u 1 m 1u 2 m 2 v v 1 n 1v 2 n 2 1 nv 2 n f 2 t u u 1 m 1u 2 m 2 v v 1 n 1v 2 n 2 a 0u 2 i 0 b 0u 2 i 1 0 a 1u 2 i 1 b 1u 2 i 1 1 0 i 0 1 m 1 a 0v 2 j 0 b 0v 2 j 1 0 a 1v 2 j 1 b 1v 2 j 1 1 0 j 0 1 n 1 here f 1 f 2 c 0 1 xr m n r r 0 our hypotheses imposed on the nonlinearities f 1 and f 2 are formulated in terms of nonnegative matrices we use fixed point index theory to establish our main results based on a priori estimates of positive solutions

nonlinear bvps with functional parameters article history received 29 may 2007 available online 6d ecember 2008 msc primary 35j65 34b15 secondary 49j40 49j60 we study the existence nonexistence and properties of solutions for a certain class of second order odes and their dependence on functional parameters also in the case when nonlinearities are in some sense singular this approach is based on variational methods and cover both sublinear and superlinear cases we develop a duality theory and variational principles for this problem as a consequence of the duality theory we give a numerical version of the variational principle which enables approximation of the solution for our problem we apply these results to obtain the existence of bounded radial and positive classical solutions for the bvp of elliptic type observe that our method allows us to investigate a certain class of elliptic systems in both bounded

higher order boundary value problems with nonhomogeneous boundary conditions abstract we study the following nonlinear boundary value problem with nonhomogeneous multi point boundary condition u 2 n g t f t u t 0 1 u 2 i 0 j 1 m a j u 2 i t j 1 i 2 i u 2 i 1 j 1 m b j u 2 i t j 1 i 2 i 1 i 0 n 1 sufficient conditions are obtained for the problem to have at least one positive solution and to have no solution respectively moreover under certain conditions we prove that there exists a bounded and continuous surface separating r 2 n 0 0 into two disjoint subsets e and n with e such that the problem has at least two positive solutions for each 0 2 n 1 e one positive solution for each 0 2 n 1 and no positive solution for any 0 2 n 1 n

existence of positive solutions for 2m order nonlinear differential systems abstract the existence of positive solutions for dirichlet boundary value problem of some nonlinear differential systems is discussed

uniqueness and nonuniqueness for positive radial solutions of δu f u r 0 on considere le probleme de l unicite pour les solutions positives du probleme de dirichlet non lineaire u f u x 0 dans u 0 est une boule ou un anneau de r n et f 0 est superlineaire en u et satisfaisait f 0 x 0

local superlinearity for elliptic systems involving parameters abstract we study the existence non existence and multiplicity of positive solutions for a class of systems of second order ordinary differential equations using the fixed point theorem of cone expansion compression type the upper lower solutions method and degree arguments we apply our abstract results to study semilinear elliptic systems in bounded annular domains with non homogeneous boundary conditions here the nonlinearities satisfy local superlinear assumptions

fuzzy topological ordered vector spaces i abstract in an ordered vector space one can consider various fuzzy topologies determined by the order relation but it is also convenient to consider the case in which in an ordered vector space a fuzzy topology is given from the beginning in this case one requires not only that the fuzzy topology be compatible with the structure of vector space but also that it be compatible with the order relation in one sense or another

positive solutions for a second order differential system this paper investigates the existence of positive solutions for a second order differential system by using the fixed point theorem of cone expansion and compression

existence of positive solutions for a class of second order ordinary differential systems abstract in this paper we present some new concepts of superlinearity and sublinearity for nonlinear terms of second order ordinary differential systems and then consider the existence of positive solutions for systems with such superlinear and sublinear nonlinear terms especially proving the existence of positive solutions for systems in which one nonlinear term is superlinear and the other is sublinear

multiple positive solutions of singularly perturbed differential systems with different orders in this paper we consider the multiplicity of positive solutions for a class of singular higher order perturbed differential systems with different orders by employing a well known fixed point theorem some new existence results are given under the case where nonlinearity can be sign changing

fuzzy topological vector spaces over r in this paper the concepts of fuzzy vector fuzzy vector space and fuzzy topological vector space are investigated a topology called sendograph topology which is compatible with the algebraic structure is given

positive solutions for superlinear elliptic equations the existence of a positive radial solution for superlinear elliptic boundary value problem in an exterior domain is proved by the use of cone expansion fixed point theorem

on the existence of bounded positive solutions for a class of singular bvps abstract we investigate the existence and properties of solutions to a second order singular ode we base ourselves on the variational approach which enables the approximation of solutions and gives a measure of a duality gap between primal and dual functional for minimizing sequences

robust h filtering for nonlinear systems abstract a robust or h approach to filtering for nonlinear systems is considered a bound on the estimate error as a function of the disturbance energy is obtained the corresponding dynamic programming equation is a first order pde this has computational ramifications the case where the measurements are discrete time is considered also a numerical method is discussed

deterministic least squares filtering a deterministic interpretation of the kalman filtering formulas is given using the principle of least squares estimation the observed signal and the to be estimated signal are modeled as being generated as outputs of a finite dimensional linear system driven by an input disturbance postulating that the observed signal is generated by the input disturbance that has minimal least squares norm leads to a method of computing an estimate of the to be estimated output the derivation of the resulting filter is carried out in a completely self contained way the analogous approach to least squares control is also discussed

existence of positive solutions for singular boundary value problems involving the one dimensional p laplacian this paper studies the existence of positive solutions for singular dirichlet boundary value problems these results are obtained by using the global continuation theorem fixed point index theory and approximate method

nonlinear elliptic problems with critical exponent in shrinking annuli soit dans r n n 2 l anneau a x p 0 dans a u 0 sur a et u u n 2 n 2 0 u 0 dans a u n 0 quand x u 0 quand x r

positive solutions of fourth order boundary value problems with two parameters abstract in this paper the existence results of positive solutions are obtained for fourth order boundary value problem u 4 u u f t u 0 where f 0 1 r r is continuous r and satisfy

existence of positive nonradial solutions for nonlinear elliptic equations in annular domains we study the existence of positive nonradial solutions of equation a f u 0 in sia u 0 on d la where s x 6 w a 2 and is positive and superlinear at both 0 and oo we use a bifurcation method to show that there is a nonradial bifurcation with mode k at ak 0 1 for any positive integer k if is subcritical and for large k if is supercritical when is subcritical then a nehari type variational method can be used to prove that there exists a e 0 1 such that for any a e a 1 the equation has a nonradial solution on 0 a

positive solutions of singular sublinear emden fowler boundary value problems abstract this paper is about the dirichlet boundary value problem of singular sublinear emden fowler equations a necessary and sufficient condition for the existence of positive solutions to this problem has been obtained by using the method of lower and upper solutions the uniqueness of positive solutions has also been discussed

second order boundary value problems with nonhomogeneous boundary conditions ii sufficient conditions are given for the existence of solutions of the following nonlinear boundary value problem with nonhomogeneous multi point boundary condition u f t u u 0 t 0 1 u 0 i 1maiu ti 1 u 1 i 1mbiu ti 2 we prove that the whole plane r2 is divided by a continuous decreasing curve into two disjoint connected regions e and n such that the above problem has at least one solution for 1 2 has at least two solutions for 1 2 e and has no solution for 1 2 n we also find explicit subregions of e where the above problem has at least two solutions and two positive solutions respectively

positive periodic solutions of higher dimensional functional difference equations with a parameter by using krasnoselskii s fixed point theorem and upper and lower solutions method we find some sets of positive values determining that there exist positive t periodic solutions to the higher dimensional functional difference equations of the form x n 1 a n x n h n fxn n n z where a n diag a1 n a2 n am n h n diag h1 n h2 n hm n aj hj z r z z are t periodic j 1 2 m t 1 0 x z rm f r m r m where r m x1 xm t rm xj 0 j 1 2 m r x r x 0

multiple positive solutions of some boundary value problems abstract we study the existence of multiple positive solutions of the equations u t u subject to linear boundary conditions we show that there are at least two positive solutions if t u is superlinear at one end point zero or infinity and sublinear at the other applications of these results are provided to yield multiple positive solutions of some elliptic boundary value problems on an annulus

existence and multiplicity results of positive doubly periodic solutions for nonlinear telegraph system abstract in this paper the existence of positive doubly periodic solutions for nonlinear telegraph system is discussed using the method of upper and lower solutions

positive solutions for 2p order and 2q order nonlinear ordinary differential systems abstract in this paper by using krasnosel skii fixed point theorem and under suitable conditions we present the existence of single and multiple positive solutions to the following systems 1 p u 2 p a t f u t v t t 0 1 1 q v 2 q b t g u t v t t 0 1 u 2 i 0 u 2 i 1 0 0 i p 1 v 2 j 0 v 2 j 1 0 0 j q 1 where 0 0 p q n we derive two explicit intervals of and such that for any and in the two intervals respectively the existence of at least one solution to the systems is guaranteed and the existence of at least two solutions for and in appropriate intervals is also discussed

multiple solutions for equations involving bilinear coercive and compact forms with applications to differential equations abstract the existence of multiple fixed points for the coercive bilinear compact forms defined in the cone in the banach space is proved multiple applications to the integral equations derived from bvps for differential equations are provided

the deterministic interpretation of the kalman filter it is known that the kalman filter has both stochastic and deterministic interpretations whereby the deterministic interpretation relates the prediction of the filter to the response of the plant

positive solutions of second order two delay differential systems with twin parameter abstract the paper is concerned with the existence of positive solutions for a second order two delay differential systems with twin parameter firstly we present some sufficient conditions with the twin parameter belonging to an open rectangular region eigenvalue region to ensure the existence of positive solutions for the differential systems with singularity secondly we deal with the superlinear semipositone problem of the differential systems and establish the existence of positive solutions for the systems the proofs are based on a fixed point theorem in cones

robust stability for multiple model adaptive control part i the framework an axiomatic framework providing robust stability and performance bounds for a wide class of estimation based multiple model switched adaptive control emmsac algorithms is developed the approach decouples development of both the atomic control designs and the estimation processes thus permitting the usage of standard controller design and optimization approaches for these components the framework is shown to give tractable algorithms for mimo lti plants and also for some classes of nonlinear systems for example an integrator with input saturation the gain bounds obtained have the key feature that they are functions of the complexity of the underlying uncertainty as described by metric entropy measures for certain important geometries such as a compact parametric uncertainties the gain bounds are independent of the number of plant models above a certain threshold which are utilized in the implementation design processes are described for achieving a suitable sampling of the plant uncertainty set to create a finite candidate plant model set whose size is also determined by a metric entropy measure which achieves a guaranteed robustness performance

fuzzy topological vector spaces ii abstract some of the properties of fuzzy topological vector spaces are investigated also there are given necessary and sufficient conditions for a family of fuzzy sets in a vector space e to be the family of all neighborhoods of zero for a fuzzy linear topology

an elliptic problem with critical growth in domains with shrinking holes we study an elliptic problem involving critical sobolev exponent in domains with small holes we prove the existence of solutions which blow up like a volcano near the centre of each hole c 2003 elsevier inc all rights reserved

positive solutions of a system of second order boundary value problems involving first order derivatives via r n monotone matrices abstract in this paper we study the existence and multiplicity of positive solutions for the system of second order boundary value problems for nonlinear ordinary differential equations depending on first order derivatives u i f i t u 1 u 1 u n u n u i 0 u i 1 0 i 1 n here n 2 f i c 0 1 r 2 n r r 0 based on a priori estimates achieved by using integral inequalities and r n monotone matrices we use fixed point index theory to establish our main results for the above problem

fuzzy syntopogenous structures and order the study of the relationship between fuzzy topological and order structures was initiated by katsaras in j math anal appl 84 1981 44 58 in m y bakier et al proc of assiut first intern conf part viii 1990 41 61 some properties of these spaces are studied in m y bakier and k el saady fuzzy sets and systems 54 1993 213 220 is by similar manner introduced the idea of order in fuzzy topological vector spaces in another work of a s mashhour et al the study of the relationship between order and lowen fuzzy uniformities is introduced and many results are studied in this paper by similar manner we will introduce the idea of order in both the fuzzy proximity space and the fuzzy syntopogenous space and we study some properties of these spaces

existence of solutions of semilinear systems with gradient dependence via eigenvalue criteria abstract in this paper new criteria are established for the existence of positive radial solutions of a semilinear elliptic system depending on the gradient these criteria are determined by some relationships between the upper and lower bounds on suitable strips of r n of the nonlinearities of the system and the principal characteristic values of some associated linear hammerstein integral operators moreover using smoothing tools the totality of the involved cone is established

robust stability of input output systems with initial conditions we consider the development of a general nonlinear input output theory which encompasses systems with initial conditions systems are defined in a set theoretic manner from input output pairs on a doubly infinite time axis and a general construction of the initial conditions is given in terms of an equivalence class of trajectories on the negative time axis input output operators are then defined for given initial conditions and a suitable notion of input output stability on the positive time axis with initial conditions is given this notion of stability is closely related to the iss ios concepts of sontag a fundamental robust stability theorem is derived which represents a generalization of the input output operator robust stability theorem of georgiou and smith to include the case of initial conditions this includes a suitable generalization of the nonlinear gap metric some applications are given to show the utility of the robust stability theorem

solutions of semilinear elliptic problems in shrinking annuli the positive radially symmetric solutions of semilinear dirichlet problems in annuli is studied the inner radius of which is sufficiently small by means of a phase plane analysis their asymptotic behaviour is computed as the inner radius shrinks it is of particular interest in the cases where the dirichlet problem for the sphere has no non trivial solution this work extends results of bandle and peletier math ann 280 1988 1 19

positive periodic solutions of infinite delay functional differential equations depending on a parameter in this paper we employ the upper and lower solutions method to study the existence of positive periodic solutions to a system of infinite delay equations with a email protected t a t x t email protected t x t

on positive solutions of some nonlinear fourth order beam equations abstract the existence uniqueness and multiplicity of positive solutions of the following boundary value problem is considered u 4 t f t u t 0 for 0 where 0 is a constant f 0 1 0 0 is continuous

existence and multiplicity results for nonlinear boundary value problems this paper studies the existence of positive solutions for a class of boundary value problems of elliptic degenerate equations by using bifurcation and fixed point index theories in the frame of approximation arguments the criteria of the existence multiplicity and nonexistence of positive solutions are established

positive radial symmetric solutions to an exterior elliptic robin boundary value problem and application abstract we study the existence uniqueness and behavior of positive radial symmetric solutions of the exterior boundary value problem u h x f u in r n b 0 r 0 u n a u on and u x 0 as x when a 0 the robin boundary condition has a wrong sign and this makes the analysis of the problem interesting and non trivial we determine a sharp condition on the coefficient a for the existence of positive spherically symmetric solutions of the boundary value problem the important model case f u u 1 7 a 1 2 r 0 and 1 2 r 0 is related to the initial data problem in general relativity for this model case as an example of application of our results we obtain the existence and uniqueness of the conformal factor corresponding to the hamiltonian constraint equation in the case of a single black hole in the radial symmetric regime