contamination source determination in water distribution networks we consider a water distribution network where at a finite number of nodes contaminant injection can occur we consider the problem of the identification of the contaminations this problem can be considered as an optimal control problem with a networked system that is governed by a transport reaction equation the identification is based upon observations from a finite number of sensors the corresponding infinite dimensional optimization problem is defined in a hilbert space setting in order to guarantee that our optimization problem has a unique solution a quadratic regularization term is added in the objective function under certain assumptions on the relations of the travel times through the pipes we obtain a representation of this optimization problem that allows the computation of the solution on a discrete time grid by solving finite dimensional linear least squares problems on these time grids there is no discretization error since our approach is based upon an exact representation of the s

feedback boundary control of linear hyperbolic systems with relaxation we consider boundary stabilization for one dimensional systems of linear hyperbolic partial differential equations with relaxation structure such equations appear in many applications by combining weighted lyapunov functions the structure is used to derive new stabilization results the result is illustrated with an application to boundary stabilization of water flows in open canals

semipositone problems with falling zeros on exterior domains abstract we study boundary value problems of the form u k x f u x u 0 if x r 0 u 0 as x where is a positive parameter u div u is the laplacian of u x r n n 2 x r 0 k belongs to a class of c 1 functions such that lim r k r 0 and f belongs to a class of c 1 functions which are negative at the origin and have falling zeros we discuss the existence and uniqueness of nonnegative radial solutions when is large

a heterogeneous diffusive logistic model of a single species population dynamics with predation and harvesting terms abstract we study existence and multiplicity of positive solutions of a heterogeneous diffusive logistic equation with predation and harvesting terms u a u b x u 2 c u 1 m u d h x in u 0 on where a c m and d are positive constants a bounded smooth domain in r n and b x is a nonnegative function on with 0 a region such that 0 and 0 x b x 0 under the strong growth rate assumption that is when a is greater than the first eigenvalue of in 0 with dirichlet boundary condition we show that the equation has at least one positive solution for 0 d d a for some d a 0 in addition in case c a we prove some multiplicity results when m m 0 with m 0 b x d x a

non negative solutions for a class of non positone problems in the recent past many results have been established on non negative solutions to boundary value problems of the form where 0 f 0 0 positone problems in this paper we consider the impact on the non negative solutions when f 0 f u to be convex to guarantee uniqueness of positive solutions and f u to be appropriately concave for multiple positive solutions this is in contrast to the case of positone problems where the roles of convexity and concavity were interchanged to obtain similar results we further establish the existence of non negative solutions with interior zeros which did not exist in positone problems

existence and multiplicity of positive solutions for multi parameter three point differential equations system abstract in this paper we study the existence and multiplicity of positive solutions for the differential equations system x a 1 t f 1 x t y t 0 0 t 1 y a 2 t f 2 x t y t 0 0 t 1 x 0 0 x 1 1 x 1 y 0 0 y 1 2 y 2 where 0 are parameters 0 2 1 1 1 2 0 1 a 1 c 0 1 0 and f 2 c 0 0 0 the system is a semi positone problem since the nonlinear term f 1 is allowed to take negative values and a 2 t may change sign on 0 1 the results are established via fixed point index theory

existence of positive solutions for a class of semipositone problem in whole ℝn in this paper we show the existence of solution for the following class of semipositone problem p where n 3 a 0 h n 0 and f 0 0 are continuous functions with f having a subcritical growth the main tool used is the variational method together with estimates that involve the riesz potential

feedback boundary control of linear hyperbolic equations with stiff source term abstractwe consider feedback boundary control of hyperbolic systems with stiff source terms by combining weighted lyapunov functions the structure is used to derive stabilisation results in our analysis we give stabilising feedback laws that allow a robust uniform exponential stabilisation for a whole range of values of an uncertain parameter with a decay rate that is independent of the parameter in particular we are interested in the limit case when the relaxation parameter approaches zero the result is illustrated with the numerical analysis on the decay rate of the lyapunov function in terms of the stiff parameter and an application to boundary stabilisation of gas dynamics in pipes

classification of the centers their cyclicity and isochronicity for the generalized quadratic polynomial differential systems in this paper we classify the centers the cyclicity of their hopf bifurcation and the isochronicity of the polynomial differential systems in r2 of degree d that in complex notation z x iy can be written as z i z zz d 22 az2 bzz cz 2 where d 2 is an arbitrary even positive integer r and a b c c note that if d 2 we obtain the well known class of quadratic polynomial differential systems which can have a center at the origin

classification of the centers their cyclicity and isochronicity for a class of polynomial differential systems generalizing the linear systems with cubic homogeneous nonlinearities abstract in this paper we classify the centers the cyclicity of its hopf bifurcation and their isochronicity for the polynomial differential systems in r 2 of arbitrary degree d 3 odd that in complex notation z x i y can be written as z i z z z d 3 2 a z 3 b z 2 z c z z 2 d z 3 where r and a b c d c if d 3 we obtain the well known class of all polynomial differential systems of the form a linear system with cubic homogeneous nonlinearities

evolution of positive solution curves in semipositone problems with concave nonlinearities abstract we study the existence multiplicity and stability of positive solutions to u x f u x for x 1 1 u 1 0 u 1 where 0 and f 0 r is monotonically increasing and concave with f 0 0 we obtain the exact number of positive solutions as a function of f t t we follow several families of nonlinearities f for which f limt f t 0 and study how the positive solution curves to the above problem evolve also we give examples where our results apply this work extends the work of a castro and r shivaji 1988 proc roy soc edinburgh sect a108 291 302 and s h wang 1994 proc roy soc edinburgh124 no 3 507 515 by obtaining sharper results and also gives a complete study of positive solutions for concave semipositone nonlinearities

multiple solutions of some semilinear elliptic equations in slender cylindrical domains we analyze the semilinear problem ul ul 0 in 0 2l ul 0 at 0 2l where rn 1 is a bounded smooth domain and is a given nonlinearity in the limit l the solutions of that problem are related to those of the n 1 dimensional problem v v 0 in v 0 at in particular necessary and sufficient conditions on a given solution of the latter v are given for the former to have a solution ul such that ul x1 x2 xn v x2 xn as l in most part of the cylinder 0 2l related bifurcation problems and some generalizations are also considered

boundary controllability between sub and supercritical flow there are several studies of the boundary controllability of quasi linear hyperbolic systems where it is assumed that the eigenvalues of the system matrixdo not change their signs during the controlled process in this paper we consider the flow through a frictionless horizontal rectangular channel that is governed by de st venant equations and show that the state can be controlled in finite time from a stationary initial state to a given stationary terminal state in such a way that during this transition the state stays in the class of c 1 functions so in particular no shocks occur there is no restriction on the initial and terminal state so in some cases it is necessary that one or both eigenvalues of the system matrixchange the sign during the process various different cases occur control between subcritical states control between supercritical states transition from a subcritical to a supercritical state and transition from a supercritical to a subcritical state in the last two cases of a control between states of a different type one eigenvalue of the system matrixchanges its sign during the process when this happens at a boundary point during the process it is necessary to switch the type of boundary conditions we show how to construct controls where at each boundary at most one such switching is necessary

on linearized coupling conditions for a class of isentropic multiphase drift flux models at pipe to pipe intersections in this paper a general drift flux model describing a subsonic and isentropic multi phase fluid in connected pipes is considered each phase is assumed to be isentropic with its own sonic speed the components are gamma law gases with 1 for such a computational challenge at a junction is the computation of rarefaction waves which do not have a readily available analytical form firstly the well posedness of the riemann problem at the junction is discussed it is suggested that rarefaction waves should be linearized in order to obtain a more efficient numerical method for coupling such multi component flow some computational results on the dynamics of the multi phase gas in the pipes demonstrate the qualitative behavior of this approach

isochronous centers of a linear center perturbed by fifth degree homogeneous polynomials in this work we study isochronous centers of two dimensional autonomous system in the plane with linear part of center type and nonlinear part given by homogeneous polynomials of fifth degree a complete classification of the necessary conditions for the time reversible systems of this class is given in order to have an isochronous center at the origin an open problem is stated for the sufficient conditions moreover we find two nonreversible isochronous families from the center cases known all the computations in order to obtain necessary conditions for such isochronous centers are given in polar coordinates and we give a proof of the isochronicity of these systems by using different methods

structure of positive solution sets of semi positone singular boundary value problems abstract in this paper we first obtain some results on the structure of positive solution sets of some differential boundary value problems then by using these results we obtain some existence and multiplicity results for positive solutions of differential boundary value problems the method used to show the main results is that of global bifurcation theories

nonnegative solution curves of semipositone problems with dirichlet boundary conditions abstract we consider the boundary value problem u x f u x x 1 1 u 1 0 u 1 where 0 is a parameter and f c 2 0 is monotonically increasing and concave up such that f 0 0 i e is the semipositone in this paper we study the case p and p p is the supremum of the nonnegative solution and is such that f 0 f s d s 0 we discuss existence and multiplicity results for nonnegative solutions

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

exact multiplicity of positive solutions of a semipositone problem with concave convex nonlinearity abstract we study the exact multiplicity of positive solutions and bifurcation diagrams of the dirichlet boundary value problem u x f u 0 1 x 1 u 1 u 1 0 where 0 is a bifurcation parameter f c 0 c 2 0 satisfies f 0 0 semipositone and f is concave convex on 0 and is asymptotic superlinear assuming additional suitable conditions on f on the u plane we give a classification of totally three qualitatively different bifurcation diagrams a reversed s shaped curve a broken reversed s shaped curve and a monotone decreasing curve our results improve those in j shi r shivaji exact multiplicity of solutions for classes of semipositone problems with concave convex nonlinearity discrete contin dyn syst 7 2002 559 571 we also give an application to determine completely the exact multiplicity of positive solutions and bifurcation diagrams of the problem with cubic nonlinearity u x u a u b u c 0 1 x 1 u 1 u 1 0 0 a b c

computing center conditions for vector fields with constant angular speed we investigate the planar analytic systems which have a center focus equilibrium at the origin and whose angular speed is constant the conditions for the origin to be a center in fact an isochronous center are obtained concretely we find conditions for the existence of a cw commutator of the field we cite several subfamilies of centers and obtain the centers of the cuartic polynomial systems and of the families y x h1 hm x y h1 hm t and y x h2 h2n x y h2 h2n t with hi homogeneous polynomial in x y of degree i in these cases the maximum number of limit cycles which can bifurcate from a fine focus is determined

unbounded connected component of the positive solution set of nonlinear operator equation and its applications abstract in this paper by using global bifurcation theories we obtain some results for structure of positive solution set of some nonlinear equations with parameters as a result we obtain some existence results for positive solutions of the nonlinear operator equation the main result can be applied to various of differential boundary value problems to obtain the existence results for positive solutions without the assumption that the nonlinearities are positone

a quadratic lyapunov function for saint venant equations with arbitrary friction and space varying slope the exponential stability problem of the nonlinear saint venant equations is addressed in this paper we consider the general case where an arbitrary friction and space varying slope are both included in the system which lead to non uniform steady states an explicit quadratic lyapunov function as a weighted function of a small perturbation of the steady states is constructed then we show that by a suitable choice of boundary feedback controls that we give explicitly the local exponential stability of the nonlinear saint venant equations for the h 2 norm is guaranteed

penalty techniques for state constrained optimal control problems with the wave equation we consider a system that is governed by a pde of hyperbolic type namely the wave equation and is controlled by a dirichlet boundary control for the penalization of terminal constraints we compare the convergence of three penalization techniques a differentiable penalty method an exact penalization and a smoothed exact penalization the error of the solution of the differentiably penalized problem is at most of the order 1 sqrt gamma where gamma is the penalty parameter the exact penalization yields the exact solution if gamma is sufficiently large if gamma is sufficiently large for the smoothed exact penalization we obtain an error bound of the order 1 sqrt beta where beta is the additional smoothing parameter this method yields differentiable objective functions that remain uniformly strongly convex since gamma need not tend to infinity to obtain convergence we also consider the penalization of distributed inequality state constraints that prescribe an upper bound for the l infty norm of the state we prove the convergence with respect to the l 2 norm for a penalization of the constraint violation measured in the l 1 norm we use this penalization technique to prove the existence of optimal controls for the inequality state constrained problem

evolution of bifurcation curves for semipositone problems when nonlinearities develop multiple zeroes we discuss existence uniqueness and multiplicity results on positive solutions to u x email protected u x 0 for email protected 0 1 u 0 0 u 1 where l 0 is a constant and u is a smooth function satisfying 0 0 semipositone in particular we follow a class of nonlinearities u as they evolve from having one positive zero to three positive zeros and compare the corresponding bifurcation curves we establish that the bifurcation curve splits into two connected components in the critical case when u develops the second zero

on the relaxation approximation of boundary control of the isothermal euler equations we consider the isothermal euler equations without friction that simulate gas flow through a pipe we consider the problem of boundary stabilisation of this system locally around a given stationary state we present a feedback law that is linear in the physical variables and yields exponential decay of the system state for the numerical solution of hyperbolic systems of conservation laws the jin xin relaxation scheme can be used therefore we also consider the boundary stabilisation of the relaxation system by the linear riemann feedback and present numerical examples that show the rapid exponential decay of the stabilised system

linearizability conditions of a time reversible quartic like system in this paper we study the linearizability problem of polynomial like complex differential systems we give a reduction of linearizability problem of such non polynomial systems to the problem of polynomial systems applying this reduction we find some linearizability conditions for a time reversible quartic like complex system and derive from them conditions of isochronous center for the corresponding real system

on the modelling and stabilization of flows in networks of open canals in this paper we present a model for the controlled flow of a fluid through a network of canals using a coupled system of st venant equations we then generalize in a variety of ways recent results of coron d andrea novel and bastin concerning the stabilizability around equilibrium of the flow through a single channel this work is based on the theory of quasilinear hyperbolic systems and in particular on a delicate result of li ta tsien concerning the existence and decay of global classical solutions

a class of reversible cubic systems with an isochronous center abstract we study cubic polynomial differential systems having an isochronous center and an inverse integrating factor formed by two different parallel invariant straight lines such systems are time reversible we find nine subclasses of such cubic systems see theorem 8 we also prove that time reversible polynomial differential systems with a nondegenerate center have half of the isochronous constants equal to zero see theorem 3 we present two open problems

classification of the centers and isochronous centers for a class of quartic like systems abstract in this paper we classify the centers and isochronous centers for a class of polynomial differential systems in r 2 of degree d that in complex notation z x i y can be written as z i z z z d 4 2 a z 3 z b z 2 z 2 c z 4 where d 4 is an arbitrary even positive integer and a b c c note that if d 4 we obtain a special case of quartic polynomial differential systems which can have a center at the origin

computing center conditions for non analytic vector fields with constant angular speed a class of planar non analytic systems whose angular speed is constant is investigated in this paper those systems could be changed into analytic systems by two transformations and the recursive formulas to compute the lyapunov constants are given futhermore with the help of computer algebra system mathematica a class of quasi cubic systems and a class of quasi quintic systems are investigated conditions of uniform isochronous center are obtained

analysis and stabilization for networked linear hyperbolic systems of rationally dependent conservation laws in this paper for a networked linear hyperbolic partial differential equations pdes system of conservation laws the propagation periods of which are rationally dependent with coupled boundary conditions we propose a novel approach to analyze its controllability and observability in addition we propose a design method of a stabilizing controller where a boundary input with boundary valued feedback is considered first we characterize the control properties such as controllability of such a pde system in terms of the corresponding ones of a finite dimensional discrete time system defined on the boundaries of the pde system which is derived by fully exploiting the method of characteristics since the obtained discrete time system is low dimensional its analysis is relatively easier next we propose a design method of a stabilizing controller based on this discrete time system finally numerical simulations are presented to show that the proposed method is effective

positive solutions for a class of nonlinear boundary value problems with neumann robin boundary conditions abstract we consider the two point boundary value problem u x f u x 0 x 1 u 0 0 u 1 u 1 0 where 0 and 0 are parameters and f c2 0 1 we discuss the existence of nonnegative solutions for superlinear nonlinearities by developing a quadrature method we study the positone f 0 0 case as well as the semipositone f 0

nondegeneracy and uniqueness of positive solutions for robin problem of second order ordinary differential equations and its applications abstract this article studies positive solutions of robin problem for semi linear second order ordinary differential equations nondegeneracy and uniqueness results are proven for homogeneous differential equations necessary and sufficient conditions for the existence of one or two positive solutions for inhomogeneous differential equations or differential equations with concave convex nonlinearities are obtained by making use of the nondegeneracy and uniqueness results for positive solutions of homogeneous differential equations

time varying riemann solvers for conservation laws on networks abstract we consider a conservation law on a network and generic riemann solvers at nodes depending on parameters which can be seen as control functions assuming that the parameters have bounded variation as functions of time we prove existence of solutions to cauchy problems on the whole network

persistently damped transport on a network of circles in this paper we address the exponential stability of a system of transport equations with intermittent damping on a network of n geq 2 circles intersecting at a single point o the n equations are coupled through a linear mixing of their values at o described by a matrix m the activity of the intermittent damping is determined by persistently exciting signals all belonging to a fixed class the main result is that under suitable hypotheses on m and on the rationality of the ratios between the lengths of the circles such a system is exponentially stable uniformly with respect to the persistently exciting signals the proof relies on an explicit formula for the solutions of this system which allows one to track down the effects of the intermittent damping

an explicit expression of the first liapunov and period constants with applications in this paper we study systems in the plane having a critical point with pure imaginary eigenvalues and we search for effective conditions to discern whether this critical point is a focus or a center in the case of it being a center we look for additional conditions in order to be isochronous we stress that the essential differences between the techniques used in this work and the more usual ones are basically two the elimination of the integration constants when we consider primitives of functions see also remark 3 2 and the fact that we maintain the complex notation in the whole study thanks to these aspects we reach with relative ease an expression of the first three liapunov constants v3 v5 andv7 and of the first two period ones p2andp4 for a general system as far as we know this is the first time that a general and compact expression ofv7has been given moreover the use of a computer algebra system is only needed in the computation ofv7andp4 these results are applied to give a classification of centers and isochronous centers for certain families of differential equations

multiple positive solutions of the one dimensional p laplacian in this work we investigate the existence of positive solutions of the p laplacian using the quadrature method we prove the existence of multiple solutions of the one dimensional p laplacian for 0 and determine their exact number for 0 2005 elsevier inc all rights reserved

positive solutions for singular semi positone three point systems abstract in this paper we study the existence of positive solutions for a singular semi positone three point nonlinear boundary value problem system with parameter 0 under certain super linear conditions on the nonlinearities by using the fixed point index method we find 0 such that the three point boundary value problem system has at least one positive solution for 0

multiple positive solutions for a class of semipositone neumann two point boundary value problems abstract we consider the two point neumann boundary value problem u x u x x 0 1 u 0 0 u l where is a positive parameter c2 0 u 0 for u 0 and for some 0 u 0 for u we discuss existence and multiplicity results for positive solutions in particular we prove that if the set s 2n2 2 2f where n n f u u0 s ds and is the unique positive zero of f is nonempty then there exist at least 2n 1 positive solutions for each s furthermore if 0 on 0 and