on the existence and multiplicity of positive periodic solutions for first order vector differential equation abstract in this paper we consider the existence and multiplicity of positive periodic solutions for first order vector differential equation x t f t x t 0 a e t 0 under the periodic boundary value condition x 0 x here is a positive constant and f 0 r n r n is a caratheodory function some existence and multiplicity results of positive periodic solutions are derived by using a fixed point theorem in cones

remarks on first and second order periodic boundary value problems on etudie les problemes aux valeurs limites periodiques d ordre 1 et 2 suivants u f t u u 0 u 2 et u f t u u 0 u 2 u 0 u 2 on obtient l existence de solutions extremales comme limites d iterees monotones

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

periodic van der pol equation with state dependent impulses abstract conditions are given for the existence of a solution of given period to the impulsively driven van der pol equation results are obtained for impulses of varying degrees of state dependence

periodic duffing delay equations with state dependent impulses conditions are obtained for the duffing equation with delay and state dependent impulses to admit a periodic solution

nonresonance impulsive functional differential inclusions with variable times in this paper we investigate the existence of solutions for first and second order nonresonance impulsive functional differential inclusions with variable moments the proofs make use of the martelli fixed point theorem for condensing multivalued maps

oscillation criteria for a linear neutral differential equation abstract for a neutral differential equation x t a t x g t b t x h t 0 0 a t b t 0 g t t h t t a connection between oscillation properties of the differential equation and differential inequalities is established explicit nonoscillation and oscillation conditions and a comparison theorem are presented

on the existence of multiple positive entire solutions for a quasilinear elliptic systems abstract in this paper our main purpose is to establish the existence of infinitely positive bounded entire solutions of second order quasilinear elliptic systems these extend a work of zuodong yang zuodong yang existence of positive bounded entire solutions of quasilinear elliptic equations appl math comput 156 2004 743 754 which considered the single quasilinear elliptic equation these extend also a work of kawano and kusano n kawano t kusano on positive entire solutions of a class of second order semilinear elliptic systems math zeitschrift 186 3 1984 287 297 which studied the semilinear elliptic equation

the method of lower and upper solutions for systems of boundary value problems the method of lower and upper solutions for second order differential system x f t x with dirichlet boundary condition x 0 x 1 0 is used to give sufficient conditions for the existence of at least one solution

ordinary differential equations with nonlinear boundary conditions of antiperiodic type abstract the quasilinearization method is successfully applied to differential problems with nonlinear boundary conditions of antiperiodic type given are sufficient conditions under which the monotone iterations converge quadratically to a unique solution of our problem the advantage of this approach lies in the fact that the approximate solutions are obtained iteratively as solutions of the above mentioned iterations

periodic boundary value problems for second order impulsive differential systems on etudie le probleme aux valeurs limites periodiques pour un systeme d equations differentielles d ordre 2 faiblement couplees avec impulsion

periodic solution of differential equation with ϕ laplacian and state dependent impulses abstract sufficient conditions for the existence of at least one periodic solution of differential equation with laplacian z t f t z t z t for a e t 0 t r and state dependent impulses z t m i t z t t i t z t i 1 p are given here t 0 r r is an increasing homeomorphism r r 0 0 f 0 t r 2 r satisfies caratheodory conditions m i 0 t r r are continuous and i 0 t r 0 t are continuous for i 1 p p n z t lim s t z s lim s t z s the results are obtained via lower and upper functions method and schauder fixed point theorem

new oscillation criteria for first order nonlinear neutral delay differential equations some new oscillation criteria of first order nonlinear neutral delay differential equations with variable coefficients are given our results extend and improve some of the well known previously results in the literature some examples are considered to illustrate our main results

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

existence of singular positive solutions for a class quasilinear elliptic equations abstract in this paper our main purpose is to establish the existence of singular positive radial solutions of second order quasilinear elliptic equations the main results of the present paper are new and extend the previously known results

a new comparison principle for impulsive differential systems with variable impulsive perturbations and stability theory in this paper the stability properties in terms of two measures for impulsive differential systems with variable impulses are investigated a new comparison principlem which allows trajectories strike the same hypersurface finite times is established and then be applied to obtain a stability criterion finally one example is worked out to show the advantage of our results

about new analogies of gronwall bellman bihari type inequalities for discontinuous functions and estimated solutions for impulsive differential systems abstract in this article we present new integral gronwall bellman bihari type inequalities for discontinuous functions integro sum inequalities as applications we investigate estimated solutions for impulsive differential systems conditions of boundedness stability practical stability

nonlinear second order periodic boundary value problems abstract in this paper we study a periodic boundary value problem pbvp for brevity of second order it is well known that if and are upper and lower solutions respectively with then there exists a solution u such that u when nothing was known the main purpose of this paper is to consider this last case also we study the structure of the set of solutions of the pbvp in the sector when and we apply the results to the case

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

nonoscillation and positivity of solutions to first order state dependent differential equations with impulses in variable moments abstract the state dependent delay differential equation x t i 1 m p i t x t h i x t f t t 0 x 0 with state dependent impulses is under consideration sufficient conditions for positivity of solutions to the cauchy and periodic problems as well as conditions for positivity of solutions to the problem with a condition on the right end of the interval 0 are given sufficient conditions for nonoscillation of solutions to the homogeneous equation f 0 0 on the half line are formulated

oscillation criteria for first order neutral differential equations with positive and negative coefficients sufficient conditions for the oscillation of the equation ddt x t r t x t r p t x t q t x t 0 where p q r c t0 r r 0 r are obtained where r t tt q u du 1 is allowed to oscillate and the condition t0s p s q s s p u q u du ds is not necessary some examples are given which show that the results here are almost sharp

oscillation criteria for forced first order neutral differential equations with variable coefficients abstract necessary and sufficient conditions are obtained so that every solution of y t p t y t q t g y t f t is oscillatory or tends to zero or to as t the problem is considered in various ranges for p t

impulsive functional differential equations with variable times in this note a schaefer fixed point theorem is used to investigate the existence of solutions for first order impulsive functional differential equations with variable times

periodic lienard type delay equations with state dependent impulses abstract conditions are obtained for lienard type equations with delay and state dependent impulses to admit an absolutely continuous periodic solution with first derivative of bounded variation and consequently with lebesgue integrable second derivative the results are applied to josephson s equation and the nonconservative forced pendulum equation

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

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

nonexistence theorems for singular solutions of quasilinear partial differential equations on etudie les etats fondamentaux singuliers de l equation de poisson semilineaire u f u 0 et de son analogue quasi lineaire div a du du f u 0 ou est le laplacien a n dimensions et a p et f u sont des fonctions donnees

uniqueness of positive solutions for quasilinear elliptic equations when a parameter is large existence and uniqueness results are proved for positive solutions of a class of quasilinear elliptic equations in a domain n via a generalisation of serrin s sweeping principle in the case when is an annulus it is shown that the solution is radially symmetric

new results on pulse phenomena for impulsive differential systems with variable moments abstract consider the impulsive differential systems with variable moments x f t x t k x x t 0 x 0 t 0 0 x i k x t k x some sufficient conditions that guarantee the absence or presence of pulse phenomena are obtained our results in this paper generalize and improve several known results

periodic boundary value problem for first order differential equations with impulses at variable times in this paper we show the validity of the method of upper and lower solutions to obtain an existence result for a periodic boundary value problem of first order impulsive differential equations at variable times

oscillations of first order neutral differential equations with variable coefficients abstract consider the first order neutral delay differential equation d dt x t p t x t q t x t t 0 t t 0 where 0 p q c t0 r and limt t t first we obtain a necessary and sufficient condition for the oscillation of all solutions of this equation and then some applications of this result are listed our results can improve many known results in the literature

existence of positive entire solutions for singular and non singular quasi linear elliptic equation we consider the quasilinear elliptic equation div u p 2 u m x u 0 in domain rn where 0 p 1 under several hypotheses on the m x we obtain the existence of positive entire solutions

bounded positive entire solutions of singular p laplacian equations abstract we investigate singular p laplacian equations of the form div u p 2 u f x u u u 0 x r n where 1 p n 0 p 1 and give a sufficient condition for the equation to have a decaying positive entire solution by means of a supersolution and a subsolution

a class of differential equations with impulses at variable times on banach spaces abstract in this paper two typical classes of semilinear evolution equation with impulses at variable times on infinite dimensional spaces are considered introducing the reasonable pc mild solutions we discuss the local existence maximal existence interval global existence of pc mild solution for two models in addition to the pulse phenomena an example is given for demonstration

periodic solutions of nonlinear boundary value problems one of the well known techniques in the theory of nonlinear boundary value problems bvp is the method of differential inequalities or the method of upper and lower solutions the method of alternative problems a global variant of the lyapunov schmidt method has been used in the study of problems at resonance the investigation of periodic bvp s forms an important subclass of problems at resonance our aim is to combine the two approaches to discuss nonlinear problems at resonance we restrict ourselves in this paper to the discussion of periodic boundary value problems in section 1 we shall indicate the method of upper and lower solutions the results for systems are given in a general way so as to include known results and also offer new directions section 2 deals with the abstract existence results at resonance in the desired framework in section 3 we consider the scalar periodic bvp s by combining the two techniques namely alternative methods and the method of differential inequalities

a monotone method for the equation uxyz f comparison theorems for the nonlinear boundary value problem u x y z f x y z u u x u y u z u x y u y z u z x with the boundary conditions u o y z a y z u x 0 z b z x u x y 0 c x y a y 0 c 0 y a 0 z b z 0 b 0 x c x 0 are established under certain conditions then it is shown that there exist sequences of lower and upper solutions which converge uniformly and monotonically to minimal and maximal solutions respectively

monotone iterative techniques of v lakshmikantham for a boundary value problem for systems of impulsive differential difference equations by means of the monotone iterative techniques of v lakshmikantham a couple of minimal and maximal quasisolutions of a two point boundary value problem for a system of impulsive differential difference equations are constructed

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

optimization problems for an elastic plate this paper concerns optimization problems related to bi harmonic equations subject to either navier or dirichlet homogeneous boundary conditions physically in dimension two our equation models the deformation of an elastic plate which is either hinged or clamped along the boundary under load we discuss existence uniqueness and properties of the optimizers

anti periodic solutions of lienard equations with state dependent impulses abstract subject to a priori bounds lienard equations with state dependent impulsive forcing are shown to admit a unique absolutely continuous anti periodic solution with first derivative of bounded variation on finite intervals the point wise convergence of a sequence of iterates to the solution is obtained along with a bound for the rate of convergence the results are applied to josephson s and van der pol s equations

approximation of solutions for nonlinear periodic boundary value problems with discontinuous upper and lower solutions we prove that it is possible to approximate the solutions of a nonlinear periodic boundary value problem via monotone sequences starting at piecewise continuous upper and lower solutions in fact we present here two different iterative methods explicit expression of each iteration is obtained by solving some linear initial value problems

existence and nonexistence of positive radial solutions for some semilinear elliptic problems in annular domains au f x u 0 in s u 0 on xj when n is some annulus and the above conditions in 4 29 are not necessarily satisfied in fact in our main result theorem 2 4 f is not necessarily c lim f t u u may not exist or may be u rn finite and f t u could be zero for u in some finite interval 0 p we also allow lim f t u u 0 corollary 2 6 and lim f t u u may not exist in example 2 3 below u o u 0 neither lim f u u nor lim f u u exists on the other hand we show that u 0 u m

pulse accumulation in impulsive differential equations with variable times abstract we study pulse accumulation phenomena in first order impulsive differential equations and give necessary and sufficient conditions to ensure pulse accumulation in such equations

oscillation and nonoscillation in neutral equations with integrable coefficients we obtain respectively new sufficient conditions for the oscillation of all solutions and the existence of a positive solution of the neutral delay differential equation ddt t p t t q t t 0 t t0 where 0 p q c t0 r and t0 q s ds

a constructive approach to boundary value problems with state dependent impulses we investigate the non linear system of ordinary differential equations u t f t u t a e t a b subject to the state dependent impulse condition u t u t u t for t a b such that g t u t 0 and the linear two point boundary condition a u a c u b d here a b f and are given continuous vector functions g is a continuous scalar function a c are constant matrices and d is a constant vector the instants of time t where the jump occurs are determined by the equation g t u t 0 and thus are unknown a priori and essentially depend on the solution u we discuss a reduction technique allowing one to combine the analysis of existence of solutions with an efficient construction of approximate solutions at present according to the authors knowledge no numerical results for boundary value problems with state dependent impulses are available in the literature

about a generalization of bellman bihari type inequalities for discontinuous functions and their applications abstract in the present paper we introduce the conditions of solvability for chaplygin s problem with discontinuous functions in two independent variables satisfying integro sum inequalities the new type of nonlinear integral and wendroff s inequality for discontinuous functions are investigated as applications the conditions of boundedness solutions of partial differential equations of hyperbolic type with impulse influence on some hypersurfaces j r 2 are obtained some historical aspects of the theory of integro sum inequalities are presented

impulsive neutral functional differential equations with variable times abstract in this paper a fixed point theorem due to schaefer is used to investigate the existence of solutions for first and second order impulsive neutral functional differential equations with variable times