existence of positive solutions for various boundary value problems in this paper we afford a concise approach to guarantee the existence of positive solutions for nonlinear second order ordinary differential equations with respect to various boundary conditions

successive iteration of positive solution for a discontinuous third order boundary value problem in this paper we obtain a successively iterative scheme of positive solution for the nonlinear third order two point boundary value problem u q u f t u 0 u 0 a u 1 b u 0 c where f is a caratheodory function f and q satisfy some additional monotone conditions the iterative scheme starts off with zero function and is therefore useful for computation purpose the main tool is monotone iterative technique on banach space moreover the iterative scheme is independent of the existence of lower and upper solutions

existence of positive solutions for non positive higher order bvps abstract we shall provide conditions on non positive function f t u 1 u n 1 so that the boundary value problem has at least one positive solution then we shall apply this result to establish several existence theorems which guarantee the multiple positive solutions

on the existence and nonexistence of positive solutions for nonlinear sturm liouville boundary value problems abstract in this paper the existence and nonexistence results of positive solutions are obtained for sturm liouville boundary value problem p x u q x u f x u x 0 1 a u 0 b p 0 u 0 0 c u 1 d p 1 u 1 0 where p c 1 0 1 q c 0 1 p x 0 q x 0 for x 0 1 f c 0 1 r a b c d 0 are constants and satisfy a b c d 0 the discussion is based on the positivity estimation for the green s function of associated linear boundary value problem and the fixed point index theory in cones

an alternative way to test the criteria ensuring the existence of discrete time normal form in this paper an alternative version of existence condition of discrete time normal form is derived for mimo nonlinear systems the proposed condition for non singular discrete time systems is formulated in a compact form the theoretical results of the new condition are further investigated through examples

global classical solutions in chemotaxis navier stokes system with rotational flux term the coupled chemotaxis fluid system nt n ns x n c c u n x t 0 t ct c nc u c x t 0 t ut u u u p n x t 0 t u 0 x t 0 t is considered under the no flux boundary conditions for n c and the dirichlet boundary condition for u on a bounded smooth domain rn n 2 3 0 1 we assume that s x n c is a matrix valued sensitivity under a mild assumption such that s x n c s0 c0 with some non decreasing function s0 c2 0 it contrasts with the related scalar sensitivity case that does not possess the natural gradient like functional structure associated estimates based on the natural functional seem no longer available in the present work a global classical solution is constructed under a smallness assumption on c0 l and moreover we obtain boundedness and large time convergence for the solution meaning that small initial concentration of chemical forces stabilization

aggregation vs global diffusive behavior in the higher dimensional keller segel model abstract we consider the classical parabolic parabolic keller segel system u t u u v x t 0 v t v v u x t 0 under homogeneous neumann boundary conditions in a smooth bounded domain r n it is proved that in space dimension n 3 for each q n 2 and p n one can find e 0 0 such that if the initial data u 0 v 0 satisfy u 0 l q e and v 0 l p e then the solution is global in time and bounded and asymptotically behaves like the solution of a discoupled system of linear parabolic equations in particular u v approaches the steady state m m as t where m is the total mass m u 0 of the population moreover we shall show that if is a ball then for arbitrary prescribed m 0 there exist unbounded solutions emanating from initial data u 0 v 0 having total mass u 0 m

boundedness and asymptotic behavior to a chemotaxis fluid system with singular sensitivity and logistic source abstract in this paper we consider the following chemotaxis fluid model with singular sensitivity and logistic source n t u n n n c c r n n k x t 0 c t u c c c n x t 0 u t u u u p n x t 0 u 0 x t 0 in a bounded domain r n n 2 3 with smooth boundary under the non flux boundary conditions for n and c and the non slip boundary condition for u we establish the global boundedness and the time decay rates of the classical solutions for any k 1 provided that satisfies suitable restrictions

global existence and boundedness in a keller segel stokes system involving a tensor valued sensitivity with saturation the 3d case abstract in this paper we continue to deal with the initial boundary value problem for the coupled keller segel stokes system n t u n n n s x n c c x t 0 t c t u c c c n x t 0 t u t p u n x t 0 t u 0 x t 0 t where r d is a bounded domain with smooth boundary and the chemotactic sensitivity s is not a scalar function but rather attains values in r d d and satisfies s x n c c s 1 n with some c s 0 and 0 when d 2 our previous work j differential equations 2015 has established the existence of global bounded classical solutions under the subcritical assumption 0 which is consistent with the corresponding results of the fluid free system but the method seems to be invalid in the three dimensional setting in this paper for the case d 3 we develop a new method to establish the existence and boundedness of global classical solutions for arbitrarily large initial data under the assumption 1 2 which is slightly stronger than the corresponding subcritical assumption 1 3 on the fluid free system where such an assumption is essentially necessary and sufficient for the existence of global bounded solutions the key idea here is to establish the general l p regularity of u from a rather low l p regularity of n which will be obtained by a new combinational functional

global existence and large time behavior for a two dimensional chemotaxis navier stokes system abstract this paper concerns the coupled chemotaxis navier stokes system in the two dimensional setting such a system was proposed in 19 to describe the collective effects arising in bacterial suspensions in fluid drops under some basic assumptions on the parameter functions k and the potential function which are consistent with those used by the experimentalists but weaker than those appeared in the known mathematical works we establish the global existence of weak solutions and classical solutions for both the cauchy problem and the initial boundary value problem supplemented with some initial data for the initial boundary value problem we also assert that the solution converges in large time to the spatially homogeneous equilibrium n 0 0 0 with n 0 1 n 0 x d x our results also show that the large diffusion of the cell density or the chemical concentration can rule out the finite time blow up even though the navier stokes fluid is included

static output feedback and guaranteed cost control of a class of discrete time nonlinear systems with partial state measurements abstract in this paper both the static output feedback issue and the observer based control of a class of discrete time nonlinear systems are considered thanks to a newly developed linearization lemma it is shown that the solution of the discrete time output feedback problem is conditioned by a set of simple convex optimization conditions that are numerically tractable and free from any equality constraint an illustrative example is provided to show the usefulness of the proposed control designs

authors reply to comments on on the discrete time normal form kotta 2000 commented on the above paper by califano et al 1998 kotta made two main criticisms in this paper the original authors reply to them

boundedness in a chemotaxis model with oxygen consumption by bacteria abstract this paper deals with the keller segel model u t u u v x t 0 v t v u v x t 0 under homogeneous neumann boundary conditions in a smooth bounded domain r n n 2 with nonnegative initial data u 0 v 0 w 1 r 2 for some r n u 0 l 1 0 and v 0 l 0 this model describes bacteria movement toward the concentration gradient of the oxygen that is consumed by the bacteria it is proved that if 0 1 6 n 1 v 0 l then the corresponding initial boundary value problem possesses a unique global solution that is uniformly bounded

linearization of discrete time systems the algebraic formalism developed in this paper unifies the study of the accessibility problem and various notions of feedback linearizability for discrete time nonlinear systems the accessibility problem for nonlinear discrete time systems is shown to be easy to tackle by means of standard linear algebraic tools whereas this is not the case for nonlinear continuous time systems in which case the most suitable approach is provided by differential geometry the feedback linearization problem for discrete time systems is recasted through the language of differential forms in the event that a system is not feedback linearizable the largest feedback linearizable subsystem is characterized within the same formalism using the notion of derived flag of a pfaffian system a discrete time system may be linearizable by dynamic state feedback though it is not linearizable by static state feedback necessary and sufficient conditions are given for the existence of a so called linearizing output which in turn is a sufficient condition for dynamic state feedback linearizability

the small convection limit in a two dimensional chemotaxis navier stokes system this paper deals with an initial boundary value problem for the chemotaxis navier stokes system begin aligned left begin array lcll n t u cdot nabla n delta n nabla cdot n nabla c qquad quad x in omega t 0 c t u cdot nabla c delta c nc qquad quad x in omega t 0 u t kappa u cdot nabla u delta u nabla p n nabla phi qquad quad x in omega t 0 nabla cdot u 0 qquad quad x in omega t 0 end array right end aligned in a bounded convex domain omega subset mathbb r 2 with smooth boundary with kappa in mathbb r and a given smooth potential phi omega rightarrow mathbb r it is known that for each kappa in mathbb r and all sufficiently smooth initial data this problem possesses a unique global classical solution n kappa c kappa u kappa the present work asserts that these solutions stabilize to n 0 c 0 u 0 uniformly with respect to the time variable more precisely it is shown that there exist mu 0 and c 0 such that whenever kappa in 1 1 begin aligned big vert n kappa cdot t n 0 cdot t big vert l infty omega big vert c kappa cdot t c 0 cdot t big vert l infty omega quad big vert u kappa cdot t u 0 cdot t big vert l infty omega le c kappa e mu t end aligned for all t 0 this result thereby provides an example for a rigorous quantification of stability properties in the stokes limit process as frequently considered in the literature on chemotaxis fluid systems in application contexts involving low reynolds numbers

multiscale models of taxis driven patterning in bacterial populations spatially distributed populations of various types of bacteria often display intricate spatial patterns that are thought to result from the cellular response to gradients of nutrients or other attractants in the past decade a great deal has been learned about signal transduction metabolism and movement in e coli and other bacteria but translating the individual level behavior into population level dynamics is still a challenging problem however this is a necessary step because it is computationally impractical to use a strictly cell based model to understand patterning in growing populations since the total number of cells may reach 10 12 10 14 in some experiments in the past phenomenological equations such as the patlak keller segel equations have been used in modeling the cell movement that is involved in the formation of such patterns but the question remains as to how the microscopic behavior can be correctly described by a macroscopic equation significant progress has been made for

positive solution for singular boundary value problems abstract a sufficient condition for the existence of positive solutions of the nonlinear boundary value problem u t f t u t 0 0 u 0 u 1 0 is constructed where f 0 1 0 0 is continuous f t u is locally lipschitz continuous and f t u u is strictly decreasing in u 0 for each t 0 1

multiplicity results for some second order four point boundary value problems abstract in this paper by using a fixed point theorem of functional type in a cone some new results for the multiplicity of positive solutions of second order four point boundary value problems are obtained the emphasis is put on the nonlinear term involved with the first order derivative

positive solutions to singular system with four point coupled boundary conditions abstract existence of positive solution to a nonlinear singular system with four point coupled boundary conditions of the type x t f t x t y t t 0 1 y t g t x t y t t 0 1 x 0 0 x 1 y y 0 0 y 1 x is established the nonlinearities f g 0 1 0 0 0 are continuous and singular at t 0 t 1 while the parameters satisfy 0 1 0 1 an example is included to show the applicability of our result

on the existence of positive solutions for semilinear elliptic equations in the annulus abstract we study the existence of positive radial solutions of u g x u 0 in annuli with dirichlet dirichlet neumann boundary conditions we prove that the problems have positive radial solutions on any annulus if is sublinear at 0 and

successive iteration and positive solution for nonlinear second order three point boundary value problems in this paper we study the existence of positive solution for two classes of nonlinear second order three point boundary value problems using some monotone iterative schemes in both cases such schemes start off with known constant functions and therefore are useful to computation purpose

nonlinear boundary value problems in hilbert spaces abstract in this paper we examine nonlinear two point boundary value problems with sturm liouville type boundary conditions in a hilbert space our technique involves using the topological transversality theorem of a granas which relies on the notions of an essential map and a priori bounds on solutions we obtain existence results for a wide class of problems with our nonlinear term satisfying a bernstein nagumo growth condition

a linear algebraic framework for the analysis of discrete time nonlinear systems a linear algebraic framework for the analysis of synthesis type problems for discrete time nonlinear systems is introduced this is an extension of a similar tool for continuous time systems that established important connections between many algorithms associated with right invertibility left invertibility and dynamic decoupling as well as between these algorithms and an approach based upon differential algebra a similar payoff is seen to be possible in the discrete time setting

three positive solutions for second order m point boundary value problems for the second order m point boundary value problemu t f t u 0 0 0 i 1 2 m 2 0 x 1 x 2 x m 2 1 growth conditions are imposed on f which yield the existence of at least three positive solutions by using the leggett williams fixed point theorem the associated green s function for the m point boundary value problem is also given

an application of topological transversality to non positive higher order difference equations in this paper we shall provide sufficient conditions on the non positive function i u 1 u n 1 so that the boundary value problem bvp given by e d nu i m i u i du i d n 2 i 0 and bc d mu 0 0 0 m n 3 a d n 2 0 b d n 1u 0 0 c d n 2u t 1 d d n 1u t 1 0 has at least one positive solution

global weak solutions for the three dimensional chemotaxis navier stokes system with nonlinear diffusion we consider an initial boundary value problem for the incompressible chemotaxis navier stokes equations generalizing the porous medium type diffusion model nt u n nm n c c x t 0 ct u c c nf c x t 0 ut u u u p n x t 0 u 0 x t 0 in a bounded convex domain r3 here r w1 0 c2 0 and 0 f c1 0 with f 0 0 it is proved that under appropriate structural assumptions on f and for any choice of m 23 and all sufficiently smooth initial data n0 c0 u0 the model possesses at least one global weak solution

boundedness in quasilinear keller segel systems of parabolic parabolic type on non convex bounded domains abstract this paper deals with the quasilinear fully parabolic keller segel system u t d u u s u v x t 0 v t v v u x t 0 under homogeneous neumann boundary conditions in a bounded domain r n with smooth boundary n n the diffusivity d u is assumed to satisfy some further technical conditions such as algebraic growth and d 0 0 which says that the diffusion is allowed to be not only non degenerate but also degenerate the global in time existence and uniform in time boundedness of solutions are established under the subcritical condition that s u d u k u e for u 0 with 2 n k 0 and e 0 when d 0 0 this paper represents an improvement of tao and winkler 17 because the domain does not necessarily need to be convex in this paper in the case r n and d 0 0 uniform in time boundedness is an open problem left in a previous paper 7 this paper also gives an answer to it in bounded domains

second and higher order systems of boundary value problems abstract existence results for systems of kth order boundary value problems are presented our analysis is based on a nonlinear alternative of a granas and use of a priori bounds

on the discrete time normal form necessary and sufficient conditions under which the discrete time normal form exists are set both in geometric and in algebraic frameworks leading to equivalent conditions the results are therefore extended to generic nonlinear nonaffine continuous time systems