quasilinear hyperbolic parabolic equations of one dimensional viscoelasticity abstract we study the global existence of solutions of initial boundary value problems for a quasilinear hyperbolic parabolic equation describing the longitudinal motion of a one dimensional viscoelastic rod we treat a variety of nonhomogeneous boundary conditions requiring separate analyses because they lead to distinctive physical effects we employ a constitutive equation giving the stress as a general nonlinear function of the strain and the strain rate all global analyses of this and related problems except that of dafermos j differential equations 1969 71 86 have employed a stress that is merely affine in the strain rate dafermos s assumptions are far more appropriate for shearing motions than for longitudinal motions our constitutive equation satisfies the physically natural requirement that an infinite amount of compressive stress is needed to produce a total compression at any point of the rod this requirement is the source of a severe singularity in the governing partial differential equations which is particularly acute when time dependent dirichlet data are prescribed the further novel yet physically reasonable restrictions we impose on the constitutive function yield estimates that preclude a total compression anywhere at any finite time the resulting estimates are crucial for the global existence theory we obtain

multiplicity results for second order two point boundary value problems with superlinear or sublinear nonlinearities we consider boundary value problems for nonlinear second order differential equations of the form u a t f u 0 t epsilon 0 1 u 0 u 1 0 where a epsilon c 0 1 0 infinity and f r r is continuous and satisfies f s s 0 for s not equal 0 we establish existence and multiplicity results for nodal solutions to the problems if either f 0 0 f infinity infinity or f 0 infinity f 0 0 where f s s approaches f 0 and f infinity as s approaches 0 and infinity respectively we use bifurcation techniques to prove our main results c 2004 elsevier inc all rights reserved

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

nodal solutions to nonlinear eigenvalue problems on time scales abstract using global bifurcation theory we obtain the existence of solutions with specified numbers of simple generalized zeros for the nonlinear eigenvalue problem on time scales t u t q t u t r f u t t t u 0 u 1 0 where r 0 is a given constant in addition we argue that our existence theorem is a generalization of a previous result which shows the existence of at least one positive solution for the above problem

existence of positive solutions for first order discrete periodic boundary value problems with delay abstract let t 3 be a positive integer and t 0 1 2 t 1 we prove the existence of positive periodic solutions of the nonlinear discrete boundary value problem u t a t g u t u t b t f u t t t t u 0 u t our approach is based upon the global bifurcation techniques

existence of nodal solutions of a nonlinear eigenvalue problem with indefinite weight function abstract we investigate the existence of nodal solutions of an indefinite weight boundary value problem u r h t f u 0 0 t 1 u 0 u 1 0 where h c 0 1 changes sign the proof of our main result is based upon bifurcation techniques

nonconstant radial positive solutions of elliptic systems with neumann boundary conditions let br be the ball of radius r in rn with n 2 we consider the nonconstant radial positive solutions of elliptic systems of the form u u f u v inbr v v g u v inbr u v 0on br where f and g are nondecreasing in each component with few assumptions on the nonlinearities we apply bifurcation theory to show the existence of at least one nonnegative nonconstant and nondecreasing solution

how to select and how to rank projects the promethee method abstract in this paper we present the promethee methods a new class of outranking methods in multicriteria analysis their main features are simplicity clearness and stability the notion of generalized criterion is used to construct a valued outranking relation all the parameters to be defined have an economic signification so that the decision maker can easily fix them two ways of treatment are proposed it is possible to obtain either a partial preorder promethee i or a complete one promethee ii both on a finite set of feasible actions a comparison is made with the electre iii method the stability of the results given by the two methods is analysed numerical applications are given in order to illustrate the properties of the new methods and some further problems are discussed

a new method for group decision support based on electre iii methodology abstract group decision is usually understood as the reduction of different individual preferences on a given set to a single collective preference at present there are few approaches which solve the group ranking problem with multiple criteria in a widely acceptable way often they rest on a poor heuristic which makes a decision about consensus ranking difficult to support this paper presents an extension of the electre iii multicriteria outranking methodology to assist a group of decision makers with different value systems to achieve a consensus on a set of possible alternatives our proposal starts with n individual rankings and n corresponding valued preference functions and uses the natural heuristic provided by electre methodology for obtaining a fuzzy binary relation representing the collective preference a comparison of this method with promethee ii for group decision is carried out we found that in this particular application the proposed heuristic based on majority rules combined with concessions to significant minorities performs relatively better than a compensatory scheme based on a net flow weighted sum function

existence and nonexistence of solutions of second order nonlinear boundary value problems abstract we study the nonlinear boundary value problem consisting of the equation y q t y w t f y on a b and a general separated homogeneous linear boundary condition by comparing this problem with a corresponding linear sturm liouville problem we obtain conditions for the existence and nonexistence of solutions of this problem more specifically let n n 0 1 2 be the n th eigenvalues of the corresponding linear sturm liouville problem then under certain assumptions the boundary value problem has a solution with exactly n zeros in a b if n is in the interior of the range of f y y y 0 and does not have any solution with exactly n zeros in a b if n is outside of the range of f y y y 0 these conditions become necessary and sufficient when f y y is monotone the existences of multiple and even an infinite number of solutions are derived as consequences we also discuss the changes of the number and the types of nontrivial solutions as the interval a b shrinks as q increases in a given direction and as the boundary condition changes

nodal solutions for second order m point boundary value problems with nonlinearities across several eigenvalues abstract we study the existence of nodal solutions of the m point boundary value problem u f u 0 0 t 1 u 0 0 u 1 i 1 m 2 i u i where i q i 1 2 m 2 with 0 1 2 m 2 1 and i r i 1 2 m 2 with i 0 and 0 i 1 m 2 i 1 we give conditions on the ratio f s s at infinity and zero that guarantee the existence of nodal solutions the proofs of our main results are based upon bifurcation techniques

radially symmetric motions of nonlinearly viscoelastic bodies under live loads this paper treats radially symmetric motions of nonlinearly viscoelastic circular cylindrical and spherical shells subjected to the live loads of centrifugal force and time dependent hydrostatic pressures the governing equations are exact versions of those for 3 dimensional continuum mechanics so shell does not connote an approximate via some shell theory these motions are governed by quasilinear third order parabolic hyperbolic equations having but one independent spatial variable the principal part of such a partial differential equation is determined by a general family of nonlinear constitutive equations the presence of strains in two orthogonal directions requires a careful treatment of constitutive restrictions that are physically natural and support the analysis the interaction of geometrically exact formulations the compatible use of general constitutive equations for material response and the presence of live loads show how these factors play crucial roles in the behavior of solutions in particular for different kinds of live loads there are thresholds separating materials that produce qualitatively different dynamical behavior the analysis using classical methods covers infinite time blowup for cylindrical shells subject to centrifugal forces infinite time blowup for cylindrical shells subject to steady and time dependent hydrostatic pressures finite time blowup for spherical shells subject to steady and time dependent hydrostatic pressures and the preclusion of total compression this paper concludes with a sketch using some modern methods of the existence of regular solutions until the time of blowup

extensions of the prudence principle to exploit a valued outranking relation abstract in many outranking methods the alternatives are first compared pairwise to build a valued outranking relation which is then exploited to derive a recommendation for the decision maker this paper proposes extensions of arrow and raynaud s prudence principle to exploit a valued outranking relation even in cases where the outranking values have an ordinal interpretation the idea is to build a ranking that maximizes the weakest support for its implicit pairwise comparisons we present a family of exploitation models providing three types of solutions depending on the decision maker s request a linear order a weak order or a partial preorder an algorithm is provided which solves the exploitation models relations between these models and some of their properties are also discussed

on thermodynamic active control of shape memory alloy wires we propose a model for the control of high frequency oscillations in shape memory alloy wires we introduce a notion of generalized solution for a generalized control and in this context prove a local exact controllability result effectively corresponding to an approximate controllability result for the nonconvex pseudoelastic material system

sharp conditions for the existence of sign changing solutions to equations involving the one dimensional p laplacian abstract we consider the boundary value problem involving the one dimensional p laplacian u p 2 u a x f u 0 0 x 1 u 0 u 1 0 where p 1 we establish sharp conditions for the existence of solutions with prescribed numbers of zeros in terms of the ratio f s s p 1 at infinity and zero our argument is based on the shooting method together with the qualitative theory for half linear differential equations

a note on bifurcation from an interval we study the global bifurcation of nonlinear sturm liouville problems of the form pu qu lambda a x f u b 0 u 0 c 0 u 0 0 b 1 u 1 c 1 u 1 0 which are not linearizable in any neighborhood of the origin c 2005 published by elsevier ltd

nodal solutions of multi point boundary value problems abstract we study the nonlinear boundary value problem consisting of the equation y w t f y 0 on a b and a multi point boundary condition by relating it to the eigenvalues of a linear sturm liouville problem with a two point separated boundary condition we obtain results on the existence and nonexistence of nodal solutions of this problem we also discuss the changes in the existence question for different types of nodal solutions as the problem changes

existence of nodal solutions for lidstone eigenvalue problems abstract we are concerned with determining values of r for which there exist nodal solutions of the lidstone eigenvalue problem 1 m u 2 m x r a x f u x 0 x 1 u 2 i 0 u 2 i 1 0 i 0 1 2 m 1 the proof of our main result is based upon eigenvalue theory and bifurcation techniques

variable consistency dominance based rough set approach to preference learning in multicriteria ranking abstract we present a methodology for non statistical preference learning in multicriteria ranking based on variable consistency dominance based rough set approach vc drsa a finite set of objects to be ranked is evaluated by a set of criteria which are real valued functions with ordinal or cardinal scales given the statement of a multicriteria ranking problem the only objective information one can get is the dominance relation over the set of objects the dominance relation is however too poor because it leaves many objects incomparable to enrich this relation and make the objects more comparable a decision maker dm must supply some preference information revealing her his value system with respect to multicriteria evaluations we are considering a frequent case when the preference information has the form of pairwise comparisons of some objects relatively well known to the dm called reference objects this information is thus composed of some decision examples on the reference objects it is the input data for a method that learns the preferences of the dm since this information is prone to inconsistencies we propose to structure it using vc drsa then the pairs of objects that are sufficiently consistent serve as a basis for induction of a preference model this model has the form of a set of if then decision rules application of these rules on the whole set of objects to be ranked yields a fuzzy preference structure directed weighted graph this preference structure is then exploited using a ranking method so as to work out a final recommendation we propose a list of properties that helps to choose a proper ranking method the methodology is illustrated by an example

self sustained oscillations of nonlinearly viscoelastic layers we study the motion of an incompressible nonlinearly viscoelastic layer subject to a slip stick frictional force applied to one of its faces by a moving belt this system is governed by a third order quasi linear parabolic hyperbolic partial differential equation subject to complicated boundary conditions we use a refined version of the hopf bifurcation theorem to show that this problem admits periodic solutions for the belt speed near critical values with the number of such solutions increasing as the viscosity of the layer decreases to verify the hypotheses of this theorem we must devote considerable effort to the tricky analysis of how the spectrum of the linearized problem depends on the belt speed and material parameters our analysis is complemented with both computations and a proof of the topological fact that the computed disposition of the eigenvalues does not omit any others we complete our study with a perturbation analysis justified by the hopf bifurcation theorem

positive solutions for the p laplacian in annuli we consider the dirichlet problem for the equation p u q x f u in an annulus r n n 1 where p u div u p 2 u is the p laplacian operator p 1 with no assumption on the behaviour of the nonlinearity f either at zero or at infinity we prove existence and localization of positive radial solutions for this problem by applying schauder s fixed point theorem precisely we show the existence of at least one such solution each time the graph of f passes through an appropriate tunnel so it is easy to exhibit multiple or even infinitely many positive solutions moreover upper and lower bounds for the maximum value of the solution are obtained our results are easily extended to the exterior of a ball when n p

multiplicity results for ode s with nonlinearities crossing all but a finite number of eigenvalues on considere des equations differentielles du type suivant u x u x p u x te 1 x x 0 u 0 u 0 ou p 1 u max u 0 r et e 1 x sinx est la fonction propre correspondant a 1 ou 0 1 2 3 k denotent les valeurs propres de l operateur d 2 dx 2 a conditions aux limites nulles

global existence of smooth solution to non linear thermoviscoelastic system with clamped boundary conditions in solid like materials in this paper we prove the global existence and uniqueness of smooth solution to a system of one dimensional non linear thermoviscoelasticity which describes the thermomechanical processes in a class of solid like materials such as rubber etc the materials satisfy that both ends of the rod are fixed this assumption was proposed by dafermos in 1982 see 6 a new approach is developed to obtain the crucial estimate of the l norm of the strain u

the parabolic hyperbolic system governing the spatial motion of nonlinearly viscoelastic rods this paper treats initial boundary value problems governing the motion in space of nonlinearly viscoelastic rods of strain rate type it introduces and exploits a set of physically natural constitutive hypotheses to prove that solutions exist for all time and depend continuously on the data the equations are those for a very general properly invariant theory of rods that can suffer flexure torsion extension and shear in this theory the contact forces and couples depend on strains measuring these effects and on the time derivatives of these strains

unique global solvability for initial boundary value problems in one dimensional nonlinear thermoviscoelasticity the balance laws of mass momentum and energy are considered for a broad class of one dimensional nonlinear thermoviscoelastic materials for the initial boundary value problem corresponding to pinned endpoints held at constant temperature we establish existence and uniqueness of temporally global classical solutions for initial data of unrestricted size our approach also applies to all boundary conditions involving pinned or stress free endpoints which are either held at constant temperature or insulated an additional and novel feature of the theory is that solid like and gaseous materials are treated in a unified way

nodal solutions for nonlinear eigenvalue problems we are concerned with determining values of for which there exist nodal solutions of the boundary value problems u ra t f u 0 0 t 1 u o u 1 0 the proof of our main result is based upon bifurcation techniques

global structure of positive solutions for nonlocal boundary value problems involving integral conditions abstract in this paper we consider the nonlinear eigenvalue problems u h t f u 0 0 t 1 u 0 0 u 1 0 1 u s d a s where 0 1 u s d a s is a stieltjes integral with a nondecreasing and a t is not a constant on 0 1 h c 0 1 0 and h t 0 on any subinterval of 0 1 f c 0 0 and f s 0 for s 0 and f 0 f 0 f 0 lim s 0 f s s f lim s f s s we investigate the global structure of positive solutions by using global bifurcation techniques

a method based on multiobjective optimization for deriving a ranking from a fuzzy preference relation abstract methods for deriving final ranking from a fuzzy preference relation do not perform well in presence of irrelevant alternatives or in case of complex graphs with numerous circuits a new method for improving the quality of their prescriptions is proposed here it rests on the idea of reducing differences between a global model of preferences and a final ranking via multiobjective optimization this proposal is also more robust than others in relation to irrelevant alternatives it can be seen as an intent of reconciling two schools of thought related to decision aid one approach accepts the fuzziness of preferences the other is based on a system of axioms that model a normative rationality

on the existence of positive radial solutions for nonlinear elliptic equations in annular domains abstract we study the existence of positive radially symmetric solutions of u g x f u 0 in annulus with dirichlet dirichlet neumann boundary conditions we show that the equation has a positive radial solution on any annulus if f and f are positive and f is superlinear at 0 and

nodal solutions for a fourth order two point boundary value problem abstract we consider boundary value problems of fourth order differential equations of the form u u u h x f u 0 x r u 0 u r u 0 u r 0 where is a parameter 0 are constants with r 2 2 r 4 4 1 h c 0 r 0 with h 0 on any subinterval of 0 r f c r r satisfies f u u 0 for all u 0 and lim u f u u 0 lim u f u u f lim u 0 f u u f 0 for some f f 0 0 we use bifurcation techniques to establish existence and multiplicity results of nodal solutions to the problem

nodal solutions of second order boundary value problems with superlinear or sublinear nonlinearities abstract we consider boundary value problems for nonlinear second order differential equations of the form u a t f u 0 t 0 1 u 0 u 1 0 where a c 1 0 1 0 with a t 0 0 for some t 0 0 1 and f r r is continuous with f s s 0 for s 0 we establish existence and multiplicity results for nodal solutions of the problems if either f 0 0 f or f 0 f 0 where f s s approaches f 0 and f as s approaches 0 and respectively we use bifurcation techniques to prove our main results

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

ground state solutions for the singular lane emden fowler equation with sublinear convection term abstract we are concerned with singular elliptic equations of the form u p x g u f u u a in r n n 3 where p is a positive weight and 0 a 1 under the hypothesis that f is a nondecreasing function with sublinear growth and g is decreasing and unbounded around the origin we establish the existence of a ground state solution vanishing at infinity our arguments rely essentially on the maximum principle

global attractors for degenerate partial differential equations from nonlinear viscoelasticity abstract we study several problems for the forced motion of light uniform nonlinearly viscoelastic bodies carrying heavy attachments a reduced problem for such motions is obtained by setting the ratio of the inertia of the viscoelastic body to the inertia of the attachment equal to zero using methods from infinite dimensional dynamical systems theory we prove that the degenerate partial differential equation of this reduced problem has an attractor and that this attractor is contained in an invariant two dimensional manifold on which solutions are governed by the classical ordinary differential equation for the forced motion of a particle on a massless spring

unilateral global bifurcation phenomena and nodal solutions for p laplacian in this paper we establish a dancer type unilateral global bifurcation result for one dimensional p laplacian problem p u m t p u g t u t 0 1 u 0 u 1 0 under some natural hypotheses on the perturbation function g 0 1 r r r we show that k p is a bifurcation point of the above problem and there are two distinct unbounded continua ck and ck consisting of the bifurcation branch ck from k p 0 where k p is the k th eigenvalue of the linear problem corresponding to the above problem as the applications of the above result we study the existence of nodal solutions for the following problem p u f t u 0 t 0 1 u 0 u 1 0 moreover based on the bifurcation result of girg and takac 2008 13 we prove that there exist at least a positive solution and a negative one for the following problem div p u f x u in u 0 on

global bifurcation and multiple results for sturm liouville problems we consider the nonlinear sturm liouville boundary value problem lu t email protected t f u t 0

computing improved optimal solutions to max min flexible constraint satisfaction problems abstract the formal framework for decision making in a fuzzy environment is based on a general max min bottleneck like optimization problem proposed by zadeh it is also the basis for extending the constraint satisfaction paradigm of artificial intelligence to accommodating flexible or prioritized constraints this paper surveys refinements of the ordering of solutions supplied by the max min formulation namely the discrimin partial ordering and the leximin complete preordering a general algorithm is given which computes all maximal solutions in the sense of these relations it also sheds light on the structure of the set of best solutions moreover classes of problems for which there is a unique best discrimin and leximin solution are exhibited namely continuous problems with convex domains and so called isotonic problems noticeable examples of such problems are fuzzy linear programming problems and fuzzy pert like scheduling problems

global attractors for quasilinear parabolic hyperbolic equations governing longitudinal motions of nonlinearly viscoelastic rods abstract we prove the existence of a global attractor and estimate its dimension for a general family of third order quasilinear parabolic hyperbolic equations governing the longitudinal motion of nonlinearly viscoelastic rods carrying an end mass and subject to interesting body forces the simplest version of the equations has the form w t t n w x w x t x where n is defined on 0 r and is a strictly increasing function of each of its arguments with n as its first argument goes to 0 this limit characterizes a total compression a source of technical difficulty which new delicate a priori estimates prevent we determine how the dimension of the attractor varies with the ratio of the mass of the rod to that of the end mass giving conditions ensuring that the dimension is small the estimates of dimension illuminate asymptotic analyses of the governing equation as this mass ratio goes to 0

on the number of solutions of two classes of sturm liouville boundary value problems abstract we employ global bifurcation theory of p h rabinowitz together with sturm comparison theorem to establish multiplicity results for some classes of sturm liouville boundary value problems

global structure of positive solutions for superlinear second order periodic boundary value problems in this paper we consider the nonlinear eigenvalue problems gather u lambda h t f u 0 quad 0 0 for i 1 ldots m 2 with sum i 1 m 2 alpha i eta i 0 for t 0 in 0 1 f in c 0 infty 0 infty and f s 0 for s 0 and f 0 infty where f 0 lim s rightarrow 0 f s s we investigate the global structure of positive solutions by using the nonlinear krein rutman theorem

uniqueness of sign changing radial solutions for δu u u p 1u 0 in some ball and annulus abstract the following dirichlet problem u u u p 1 u 0 in u 0 on is considered where is either an annulus or a ball in r n and p 1 the uniqueness of radial solutions having exactly k 1 nodes is shown for the following cases is a sufficiently thin annulus is a certain small ball n 4 and 1 p n n 2 is the unit ball n 3 and 1 p 3 is any annulus or any ball but p 1 is sufficiently close to 1 and n 3 5 or 7

on the existence of multiple solutions of the boundary value problem for nonlinear second order differential equations abstract we consider the boundary value problem for nonlinear second order differential equations of the form u a x f u 0 0 u 0 u 1 0 we establish the precise condition concerning the behavior of the ratio f s s at infinity and zero for the existence of solutions with prescribed nodal properties then we derive the existence and the multiplicity of nodal solutions to the problem our argument is based on the shooting method together with the strum s comparison theorem the results obtained here can be applied to the study of radially symmetric solutions of the dirichlet problem for semilinear elliptic equations in annular domains

dynamics as a mechanism preventing the formation of finer and finer microstructure we study the dynamics of pattern formation in the one dimensional partial differential equation u u w u x x u xxt u 0 text u u x t text x in 0 1 text t 0 proposed recently by ball holmes james pego swart bhjps as a mathematical cartoon for the dynamic formation of microstructures observed in various crystalline solids here w is a double well potential like 1 4 ux 2 1 2 what makes this equation interesting and unusual is that it possesses as a lyapunov function a free energy consisting of kinetic energy plus a nonconvex elastic energy but no interfacial energy contribution which does not attain a minimum but favours the formation of finer and finer phase mixtures e u u t int limits 0 1 frac u t 2 2 w u x frac u 2 2 dx our analysis of the dynamics confirms the following surprising and striking difference between statics and dynamics conjectured in bhjps on the basis of numerical simulations of swart holmes sh while minimizing the above energy predicts infinitely fine patterns mathematically weak but not strong convergence of all minimizing sequences unvn of e u v in the sobolev space w1p 0 1 l2 0 1 solutions to the evolution equation of ball et al typically develop patterns of small but finite length scale mathematically strong convergence in w1p 0 1 l2 0 1 of all solutions u t ut t with low initial energy as time t

quasilinear equations for viscoelasticity of strain rate type we consider the quasilinear m m system of partial differential equations that governs the motion of a viscoelastic material of strain rate type on a bounded domain in mathbb r n the dependence of the stress on both the strain and strain rate is nonlinear and our hypotheses allow for a potential energy which is a nonconvex function of the strain the critical hypothesis is that the dependence of the stress function on the strain rate is uniformly strictly monotone in the sense of minty and browder we prove the existence and uniqueness of weak solutions to a natural initial boundary value problem for a large class of constitutive functions we then treat the question of h2 regularity of solutions and show that while regularity in the initial data is preserved solutions do not in general become more regular than their initial data this generalizes a result for the semilinear case due to rybka

weak solutions for a class of nonlinear systems of viscoelasticity the principal focus of the article is the construction of classical weak solutions of the initial value problem for a class of systems of viscoelasticity in arbitrary spatial dimension the class of systems studied is large enough to incorporate certain requirements dictated by frame indifference and also has a structure which allows for a variational treatment of the time discretized problem weak solutions for this system are constructed under certain monotonicity hypotheses and are shown to satisfy various a priori estimates in particular giving improved regularity for the time derivative also measure valued solutions are obtained under a uniform dissipation condition which is much weaker than monotonicity a special case of the viscoelastic system is the gradient flow of a non convex potential for which measure valued solutions are here obtained a new result in the vectorial case furthermore in this setting it is possible to show that these measure valued solutions satisfy a certain property which ensures they coincide with the classical weak solution when this exists as for example in the convex case where existence and uniqueness are well known

bifurcation of sign changing solutions for one dimensional p laplacian with a strong singular weight p sublinear at abstract in this paper we consider one dimensional p laplacian problems with a singular weight which may not be in l 1 using the properties of eigenfunctions and the global bifurcation theory we prove existence uniqueness nonexistence and multiplicity results of positive solutions as well as sign changing solutions specially when the nonlinear term is p linear near 0 and p sublinear at

on the modeling and computations of nonlinear thermodynamics in sma wires we present a mathematical model describing the thermodynamic behavior of shape memory alloy wires as well as a computational technique to solve the resulting system of partial differential equations the model consists of continuum level conservation equations based on a new construction of the helmholtz free energy potential this construction allows specification of material constants for different shape memory wires the computational technique introduces a viscosity based continuation method which allows the model to handle dynamic applications where the temporally local behavior of solutions is desired computational experiments document that this combination of modeling and solution techniques appropriately predicts the thermally and stress induced martensitic phase transitions as well as the hysteretic behavior and production of latent heat associated with such materials

existence of sign changing periodic solutions of second order difference equations abstract we are concerned with determining values of r for which there exist sign changing solutions of nonlinear periodic boundary value problems 2 u t 1 rf u t 0 t t u 0 u t u 1 u t 1 the proof of our main result is based upon global bifurcation techniques

nodal solutions of boundary value problems with boundary conditions involving riemann stieltjes integrals abstract we study the nonlinear boundary value problem consisting of the equation y i 1 m w i t f i y and a boundary condition involving a riemann stieltjes integral by relating it to the eigenvalues of the corresponding linear sturm liouville problem with a two point separated boundary condition we obtain results on the existence and nonexistence of nodal solutions of this problem the shooting method and an energy function are used to prove the main results

generating linear extensions fast one of the most important sets associated with a poset cal p is its set of linear extensions e cal p this paper presents an algorithm to generate all of the linear extensions of a poset in constant amortized time that is in time o e cp where e cp e cp the fastest previously known algorithm for generating the linear extensions of a poset runs in time o n cdot e cp where n is the number of elements of the poset the algorithm presented here is the first constant amortized time algorithm for generating a naturally defined class of combinatorial objects for which the corresponding counting problem is p complete furthermore it is shown that linear extensions can be generated in constant amortized time where each extension differs from its predecessor by one or two adjacent transpositions the algorithm is practical and can be modified to count linear extensions efficiently and to compute p x y for all pairs x y in time o n 2 e cal p

global bifurcation and nodal solutions for a sturm liouville problem with a nonsmooth nonlinearity abstract in this paper we shall establish the unilateral global bifurcation which bifurcates from the trivial solutions axis or from infinity of a class of nonlinear sturm liouville problems with nondifferentiable nonlinearity respectively as applications of the above results we shall determine the interval of r in which there exist nodal solutions for the following problem u t r a t f u 0 t 0 1 u 0 u 1 0 where a t is a positive continuous function on 0 1 f c r r but is not necessarily differentiable at the origin and infinity moreover as a special case of the above problem we shall prove more details about the existence of nodal solutions for a class of half linear eigenvalue problems

nodal solutions for singular nonlinear eigenvalue problems abstract we are concerned with determining values of r for which there exist nodal solutions of the boundary value problems u r a t f u 0 0 t 1 u 0 u 1 0 where r is a parameter and a 0 1 0 is continuous and satisfies 0 0 1 t 1 t a t d t the proof of our main result is based on bifurcation techniques