multiplicity results for asymptotically linear elliptic problems at resonance in this paper several new multiplicity results for asymptotically linear elliptic problem at resonance are obtained via morse theory and minimax methods some new observations on the critical groups of a local linking type critical point are used to deal with the resonance case at 0

multiple periodic solutions of ordinary differential equations with double resonance abstract in this paper we study by morse theory the existence of multiple periodic solutions of a class of ordinary differential equation with double resonance at infinity between two consecutive eigenvalues and with resonance at origin

bifurcation and multiple solutions for perturbations of linear elliptic problems abstract combining a bifurcation theorem with a local leray schauder degree theorem of krasnoselskii and zabreiko in the case of a simple singular point we obtain an existence result on the number of small solutions for a class of functional bifurcation equations since this result contains the information of local leray schauder degree we obtain new multiplicity results for the perturbations of second order linear elliptic problems by unbounded nonlinearities as applications here by a priori bounds essentially due to gupta and by a leray schauder degree computation

nontrivial solutions for impulsive fractional differential equations via morse theory abstract in this paper we study the existence of nontrivial solutions for an impulsive fractional differential equation with dirichlet boundary conditions by using morse theory coupled with local linking arguments we obtain some new criteria to guarantee that the impulsive fractional differential equations have at least one nontrivial solution

dirichlet problems with double resonance and an indefinite potential abstract we consider semilinear dirichlet problems with an unbounded and indefinite potential and with a caratheodory reaction we assume that asymptotically at infinity the problem exhibits double resonance using variational methods together with morse theory and flow invariance arguments we prove multiplicity theorems producing three five six or seven nontrivial smooth solutions in most multiplicity theorems we provide precise sign information for all the solutions established

minimum energy trajectories of the swing ankle when stepping over obstacles of different heights this study was performed to test the hypothesis that the motion of the lower extremities when stepping over obstacles is governed by the criterion of minimum mechanical energy the trajectories of the swing ankle during level walking and when stepping over obstacles of 51 102 153 and 204 mm heights were predicted and measured for eight healthy young adults the predictions were made with a planar seven link linkage model based on the criterion of minimum mechanical energy using the method of dynamic programming when stepping over obstacles the predicted trajectories of the swing ankle were just high enough for the swing toe to clear the obstacles the clearances measured between the obstacle and toe were significantly larger than those predicted when stepping over obstacles the levels of work required to generate the measured trajectories were significantly larger p or 0 002 than those required to produce the predicted trajectories the amount of work necessary to generate the measured or predicted trajectories increased linearly significant at p or 0 022 with obstacle height and except when predicting the trajectory for the lowest obstacle was significantly greater than that required when walking on level ground p 0 02 thus conservation of energy was found to become a less dominant criterion for governing the motion of the body when crossing obstacles than when walking on level ground

solutions of asymptotically linear operator equations via morse theory abstract in this paper we use the classical morse theory of critical points to study the existence and multiplicity of solutions of a class of asymptotically linear operator equations as special cases we include multiplicity results for semilinear elliptic bvp s as well as existence and multiplicity of periodic solutions of semilinear wave equation and of hamiltonian systems these results simplify and complement recent work of amann zehnder and castro lazer author

critical groups at zero and multiple solutions for a quasilinear elliptic equation abstract in this paper by morse theory we will compute the critical groups at zero for a functional i w 0 1 p r defined by setting i u 1 p u p d x 1 2 u 2 d x f x u d x where p 2 is a bounded domain in r n f x u 0 u f x t d t and we assume that f is resonant at zero for the spectrum of in w 0 1 2 as an application of these critical groups estimates some multiplicity results are also given

an elliptic resonance problem with multiple solutions in this paper we study the existence of multiple nontrivial solutions for a semilinear elliptic equation at resonance by the minimax methods and morse theory

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

asymptotically linear elliptic equations without nonresonance conditions abstract in this paper we are concerned with the existence of nontrivial solutions of a semilinear elliptic equation when the nonresonance condition at infinity is not satisfied we consider a strongly resonant case in the first part and a sort of resonance under density assumptions in the second part

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

pairs of nontrivial solutions for resonant neumann problems abstract we study a semilinear neumann problem which is resonant at with respect to any eigenvalue different from the first and the second eigenvalue of n the negative neumann laplacian using a combination of variational methods with morse theoretic techniques we show that the problem has at least two nontrivial smooth solutions

nonselfadjoint resonance problems with unbounded perturbations soit un domaine borne de r n n 1 a frontiere de classe c 2 pour 0 1 soit lu i 1 n j 1 n a idj x 2 u x i x j i 1 n b i x u x i a 0 x u ou a ij x a ji x 1 i j n a 0 x 0 sur et i 1 n j 1 n a ij x i j 0 pour x et r n 0 on considere le probleme lu 1 u g u h u 0 ou 1 est la valeur propre principale de l h c et g est localement lipschitzien sur

multiple solutions for semilinear resonance elliptic problems with nonconstant coefficients at infinity in this paper we study a class of semilinear elliptic equations which are completely resonant with nonconstant coefficients at origin and at infinity by applying morse theory and minimax method we obtain the existence of multiple nontrivial solutions for the equations

solutions to a gradient system with resonance at both zero and infinity in this paper we study the existence and multiplicity of nontrivial solutions for a gradient system with resonance at both zero and infinity via morse theory

multiple solutions for semilinear elliptic boundary value problems with double resonance abstract in this paper we study the multiplicity of nontrivial solutions of semilinear elliptic boundary value problems which may be double resonance near infinity between two consecutive eigenvalues of with zero dirichlet boundary data the methods we use here are morse theory minimax methods and bifurcation theory

metrisability of two dimensional projective structures we carry out the programme of r liouville 19 to construct an explicit local obstruction to the existence of a levi civita connection within a given projective structure on a surface the obstruction is of order 5 in the components of a connection in a projective class it can be expressed as a point invariant for a second order ode whose integral curves are the geodesics of or as a weighted scalar projective invariant of the projective class if the obstruction vanishes we find the sufficient conditions for the existence of a metric in the real analytic case in the generic case they are expressed by the vanishing of two invariants of order 6 in the connection in degenerate cases the sufficient obstruction isof order at most 8

applications of local linking to critical point theory we prove the existence of nontrivial critical points of functionals with a local linking at 0 applications to elliptic boundary value problems and to hamiltonian systems are given c 1995 academic press inc

existence of a nontrivial solution for a class of hemivariational inequality problems at double resonance abstract in this paper we discuss a class of semilinear elliptic hemivariational inequality problems by using the nonsmooth minimax principle for locally lipschitz functions we establish the existence of a nontrivial solution for the semilinear elliptic hemivariational inequality problem where incomplete double resonance occurs at infinity between two distinct consecutive eigenvalues

an asymmetric superlinear elliptic problem at resonance abstract in this article we study the existence and multiplicity of solutions to the problem u g x u in u 0 on where is a bounded domain in r n n 2 with smooth boundary and g r r is a differentiable function we will assume that g x s has a resonant behavior for large negative values of s and that a landesman lazer type condition is satisfied we also assume that g x s is superlinear but subcritical for large positive values of s we prove the existence and multiplicity of solutions for problem 1 1 by using minimax methods and infinite dimensional morse theory

on a robin problem with indefinite weight and asymmetric reaction superlinear at abstract the existence of at least three nontrivial smooth solutions to a semilinear robin problem with indefinite potential and asymmetric nonlinearity super linear at is established both crossing and resonance are allowed proofs exploit variational methods truncation techniques and morse theory

on solvability for a class of quasilinear resonance elliptic equations abstract in this paper we obtain an existence result for a class of high order quasilinear elliptic equations with higher eigenvalues the proofs rely on galerkin type techniques brouwer s fixed points theorem in this case the nonlinearity is unbounded and satisfies sublinear growth the equation is one of the most useful sets of navier stokes equations which describe the motion of viscous fluid substances such as liquids gases and so on

computations of critical groups and applications to some differential equations at resonance abstract in this paper we first consider the computations of the critical groups of a functional with generalized ahmad lazer paul type conditions both at zero and infinity then the abstract results are applied to investigate some new cases of the existence of nontrivial solutions of the second order hamiltonian systems and elliptic boundary value problems which may be resonant both at zero and infinity

multiple solutions to a robin problem with indefinite weight and asymmetric reaction abstract the existence of two nontrivial smooth solutions to a semilinear robin problem with indefinite unbounded potential and asymmetric nonlinearity f is established both crossing and resonance are allowed a third nonzero solution exists provided f is c 1 proofs exploit variational methods truncation techniques and morse theory

multiple nontrivial solutions for asymptotically linear discrete problem via computations of the critical groups in this paper we study the multiplicity of nontrivial solutions for asymptotically linear discrete problem by using critical point theory morse theory and minimax methods we obtained that the problem has at least two nontrivial solutions under various conditions

robin problems with a general potential and a superlinear reaction abstract we consider semilinear robin problems driven by the negative laplacian plus an indefinite potential and with a superlinear reaction term which need not satisfy the ambrosetti rabinowitz condition we prove existence and multiplicity theorems producing also an infinity of smooth solutions using variational tools truncation and perturbation techniques and morse theory critical groups

one sided resonance problems for quasilinear elliptic operators we present some new existence results for a quasilinear elliptic problem with an unbounded driving force the quasilinear elliptic operator is assumed to be variational and is such that 0 acts like an isolated eigenvalue with a corresponding eigenfunction which does not change sign the driving force is further assumed to be in one sided resonance around the eigenvalue 0 and a solvability condition of potential type is imposed variational methods are used to obtain existence our results significantly improve earlier results of the authors

predicting the kinematics and kinetics of gait based on the optimum trajectory of the swing limb an algorithm was developed to predict the minimum energy consumption trajectory of the swing limb the method of dynamic programming a multistage optimization method was applied to generate the optimum trajectory of the swing ankle which minimized the mechanical energy required to generate the moments of the joints of the lower extremities during the single support phase of gait predictions and measurements of gait were compared for six healthy subjects the predicted hip and knee flexion angles of the swing limb were not significantly different from those experimentally measured except for hip flexion at times greater than 75 of the swing period the predicted ground reaction forces were not significantly different from the measured ground reaction forces furthermore the moments about the joints were not significantly different from those computed using the measured ground reaction forces and kinematics of the limbs the results of this study support the hypothesis that human gait is energy efficient

geodesic rigidity of conformal connections on surfaces we show that a conformal connection on a closed oriented surface sigma of negative euler characteristic preserves precisely one conformal structure and is furthermore uniquely determined by its unparametrised geodesics as a corollary it follows that the unparametrised geodesics of a riemannian metric on sigma determine the metric up to constant rescaling it is also shown that every conformal connection on the 2 sphere lies in a complex 5 manifold of conformal connections all of which share the same unparametrised geodesics

nontrivial solutions of semilinear equations at resonance in this paper we prove new existence results concerning nontrivial solutions to semilinear elliptic problem at resonance the methods used here are based on combining the minimax methods and the morse theory

nontrivial critical points for asymptotically quadratic function abstract in this paper we study the existence of nontrivial critical points as applications we study the existence of nontrivial solutions of the dirichelet problem for nonlinear elliptic pde and periodic boundary value problem for nonlinear ope

applications of morse theory to some nonlinear elliptic equations with resonance at zero abstract in this paper we study the existence and multiplicity of solutions for some nonlinear elliptic boundary value problems with resonance at zero by applying morse theory we do not impose additional global condition on the nonlinearities except for a subcritical growth condition

on resonant neumann problems we consider semilinear neumann problems at resonance and prove existence and multiplicity theorems the existence theorems allow resonance with respect to any eigenvalue of the negative neumann laplacian the multiplicity theorems concern problems resonant at 0 the principal eigenvalue or at the first nonzero eigenvalue our approach uses tools from critical point theory and from morse theory

non uniformly asymptotically linear p laplacian problems abstract we relax conditions on uniform convergences of f x s s p 2 s which are essential in many results on multiplicity for asymptotically linear p laplacian problems

nontrivial solutions for discrete boundary value problems with multiple resonance via computations of the critical groups abstract in this paper we study the existence of nontrivial solutions for a class of second order difference equations with multiple resonance at both infinity and the origin by applying the critical point theory and morse theory

power requirements and mechanical efficiency of treadmill walking abstract the instantaneous energy levels of body segments are computed from kinematic measurements on a level treadmill at various speeds with freely chosen step rates and a constant speed with different imposed step rates the changes in the energy levels of segments are combined to compute the average work rate required to accelerate the total body positive internal work this work is compared to total metabolic power consumption to obtain a minimal estimate of mechanical efficiency the efficiency increases rapidly from 9 to 0 84 m sec to a maximum of 23 at 1 70 m sec thereafter the efficiency slowly decreases with speed to 18 at 2 35 m sec when different step rates are imposed at one constant speed the average positive work rate remains constant this work rate level is identical to that required for walking at the same speed with self determined free step rate thus maximum gross efficiency results at the free step rate

minimal lagrangian connections on compact surfaces abstract we introduce the notion of a minimal lagrangian connection on the tangent bundle of a manifold and classify all such connections in the case where the manifold is a compact oriented surface of non vanishing euler characteristic combining our classification with results of labourie and loftin we conclude that every properly convex projective surface arises from a unique minimal lagrangian connection

metrisability of projective surfaces and pseudo holomorphic curves we show that the metrisability of an oriented projective surface is equivalent to the existence of pseudo holomorphic curves a projective structure mathfrak p and a volume form sigma on an oriented surface m equip the total space of a certain disk bundle z rightarrow m with a pair j mathfrak p mathfrak j mathfrak p sigma of almost complex structures a conformal structure on m corresponds to a section of z rightarrow m and mathfrak p is metrisable by the metric g if and only if g m rightarrow z is a pseudo holomorphic curve with respect to j mathfrak p and mathfrak j mathfrak p da g

nontrivial solutions of operator equations and morse indices of critical points of min max type on montre que si les hypotheses du theoreme de point selle sont satisfaites si dim y 2 et si f 1 c contient seulement des points critiques non degeneres alors f 1 c contient au moins un point critique u 0 tel que 2 indice de morse u 0 dim y

existence of solutions for a class of singular quasilinear elliptic resonance problems abstract the paper concerns a resonance problem for a class of singular quasilinear elliptic equations in weighted sobolev spaces the equation set studied is one of the most useful sets of navier stokes equations these describe the motion of viscous fluid substances such as liquids gases and so on by using galerkin type techniques the brouwer fixed point theorem and a new weighted compact sobolev type embedding theorem established by shapiro we show the existence of a nontrivial solution

resonance and nonresonance in terms of average values abstract we prove existence results for nonlinear two point boundary value problems what sets our results apart is that we impose sufficient conditions for solvability in terms of the asymptotic average values of the nonlinearities our solvability conditions allow the nonlinear term to have significant oscillations outside the given spectral gap as long as it remains within the interval on the average in some sense

multiple solutions with precise sign for nonlinear parametric robin problems we consider a parametric nonlinear robin problem driven by the p laplacian we show that if the parameter 2 the second eigenvalue of the robin p laplacian then the problem has at least three nontrivial solutions two of constant sign and the third nodal in the semilinear case p 2 we show that we can generate a second nodal solution our approach uses variational methods truncation and perturbation techniques and morse theory in the process we produce two useful remarks about the first two eigenvalues of the robin p laplacian