existence of solutions to an initial value problem for the differential equation f t x x 0 using barrier strips abstract under sign assumptions we investigate the global existence of solutions of the initial value problem f t x x x 0 a where the function f t x p may be singular at x a

on the solvability of a singular initial value problem x f t x x using barrier strips abstract in this paper conditions which guarantee the existence of solutions to x f t x x x 0 a are given

spectral properties of metastable markov semigroups abstract it is shown that if a symmetric markov semigroup e ht on the hilbert space l 2 x is hypercontractive then the approximate degeneracy of the ground state has several consequences concerning other parts of the spectrum of h and concerning the unitary group e iht in particular in the presence of a space inversion symmetry all the eigenvalues occur in pairs with gaps comparable to the gap between the bottom two eigenvalues

existence of at least three solutions of a second order three point boundary value problem abstract we study existence of at least three solutions in the presence of two lower and two upper solutions of some second order nonlinear three point boundary value problem of the type x f t x x t i 0 1 x 0 0 x 1 x 0 1 0 1 the growth of f with respect to x is allowed to be quadratic we use some degree theory arguments to get the multiplicity result

a generalized upper and lower solution method for singular initial value problems abstract this paper presents new existence results for singular initial value problems in particular our nonlinearity may be singular in its dependent variable and is allowed to change sign

comparing branch and price algorithms for the multi commodity k splittable maximum flow problem abstract the multi commodity k splittable maximum flow problem consists in routing as much flow as possible through a capacitated network such that each commodity uses at most k paths and the capacities are satisfied the problem appears in telecommunications specifically when considering multi protocol label switching the problem has previously been solved to optimality through branch and price in this paper we propose two exact solution methods both based on an alternative decomposition the two methods differ in their branching strategy the first method which branches on forbidden edge sequences shows some performance difficulty due to large search trees the second method which branches on forbidden and forced edge sequences demonstrates much better performance the latter also outperforms a leading exact solution method from the literature furthermore a heuristic algorithm is presented the heuristic is fast and yields good solution values

a generalized upper and lower solutions method and multiplicity results for nonlinear first order ordinary differential equations abstract we introduce a generalized upper and lower solutions method for the solvability of first order ordinary differential equations u t t u t u 0 u 1 in order to cover the case when the function satisfies caratheodory conditions this method is then applied to get multiplicity results when the nonlinearity interacts with the real eigenvalue of the linearized problem our proofs are based on differential inequalities and classical leray schauder degree

singular and nonsingular first order initial value problems abstract under barrier strip type arguments we investigate the existence of global solutions to the initial value problem x f t x x x 0 a where the scalar function f t x p may be singular at x a

the monotone method for first order problems with linear and nonlinear boundary conditions in this paper we develop the monotone method for the first order problem u t f t u t for a e t a b when f is a caratheodory function and u w 1 1 a b we consider the nonlinear boundary conditions l u a u b 0 with l c r 2 r nondecreasing in x or nonincreasing in y and the linear boundary conditions a 0u 0 b 0u t l 0 with a 0 b 0 and l 0 r we prove the existence of solutions and the validity of the monotone method if there exists a lower solution a and an upper solution b with either a b for the linear conditions we obtain eight new concepts of lower and upper solutions which generalize previous known cases

existence of multiple solutions for some nonlinear boundary value problems abstract by imposing one sided conditions on the nonlinearity where neither regularity nor uniformity is required we prove the existence of either a nonnegative or a nonpositive solution for first and second order ordinary differential equations with periodic neumann or dirichlet boundary conditions positone and nonpositone problems are considered some nonexistence results are also obtained when using generalized ambrosetti prodi type conditions we get the existence of nonnegative and nonpositive solutions for first and second order periodic or neumann boundary value problems our method of proof makes use of topological degree arguments in cones

upper and lower solutions with jumps abstract we study a periodic boundary value problem for a first order differential equation from a new point of view which permits us to obtain an existence result involving upper and lower solutions with jump discontinuities we present some applications of our result with illustrative examples

a multiplicity result for a nonlinear boundary value problem abstract in this paper we establish existence and multiplicity results for the problemx x f t x x s t a e in 0 x 0 x under the ambrosetti prodi type condition withfbeing a caratheodory function

existence of periodic solutions for fully nonlinear first order differential equations in this paper we establish some existence results for periodic solutions of fully nonlinear first order scalar differential equation f t x x 0 the approach here uses the viscosity solutions method developed in recent decades and the classical upper lower solutions method

existence and multiplicity results for some three point boundary value problems abstract using the method of upper and lower solutions and some degree theory arguments we establish the existence of at least three solutions of some second order nonlinear differential equations of the type x f t x x t i 0 1 subject to nonlinear three point boundary conditions x 0 0 x 1 g x 0 1 the growth of f with respect to x is allowed to be quadratic

existence of at least three solutions of nonlinear three point boundary value problems with super quadratic growth abstract we establish the existence of at least three solutions in the presence of two lower and two upper solutions of some second order nonlinear three point boundary value problem of the type x f t x x 0 t 1 x 0 0 x 1 x 0 1 0 1 we employ a condition weaker than the well known nagumo condition which allows the nonlinearity f t x x to grow faster than quadratically with respect to x in some cases our method uses some degree theory arguments

the number of periodic solutions of some analytic equations of abel type new results are proved to estimate the number of periodic solutions of a differential equation of abel type by using a modification of a technique introduced by ilyashenko the main tool is an estimate on the number of zeros of a holomorphic function a concrete example is analyzed but the results are presented to make the method flexible and applicable to other equations

existence of solutions to initial value problems for first order differential equations under sign assumptions we investigate the global existence of solutions of the initial value problem f t x x 0 x a a where the function f t x p may be singular at t a

exact multiplicity for periodic solutions of a first order differential equation abstract consider the differential equation 1 x f t x h t where h t is a 1 periodic continuous function and f t x c3 is concave convex in x and 1 periodic in t we obtain the complete structure of 1 periodic solutions by means of singularity theory more precisely we show that the image of singularities f consists of a codimension 1 manifold that divides the c r z into two open sets a1 a3 i equation 1 has a unique 1 periodic solution for h t a1 ii the equation has exactly three 1 periodic solutions for h t a3 furthermore if the image of cusp singularities f c is a codimension 1 manifold of f the differential equation has exactly two solutions for h t f f c and has a unique 1 periodic solution for h t f c

upper and lower solutions for second order boundary value problems with nonlinear boundary conditions on demontre des theoremes d existence en utilisant des solutions superieures et inferieures