existence of positive solution for nonlinear fourth order difference equations let t be an integer with t 5 and let t 2 2 3 t we show the existence and multiplicity of positive solutions of the boundary value problem of nonlinear fourth order difference equation d 4u t 2 lf t u t 0 t t 2 u 1 u t 1 d 2u 0 d 2u t 0 where l is a parameter f t 2x 0 0 is continuous

existence of positive solutions for 2nth order singular sublinear boundary value problems abstract this paper investigates the existence of positive solutions for 2nth order n 1 singular sub linear boundary value problems a necessary and sufficient condition for the existence of c 2 n 2 0 1 as well as c 2 n 1 0 1 positive solutions is given by constructing lower and upper solutions and with the maximal theorem our nonlinearity f t x 1 x 2 x n may be singular at x i 0 i 1 2 n t 0 and or t 1

existence of positive solutions for a system of generalized lidstone problems in this paper we study the existence of positive solutions for the system of generalized lidstone problems for ordinary differential equations 1 mu 2 m f 1 t u u 1 m 1u 2 m 2 v v 1 n 1v 2 n 2 1 nv 2 n f 2 t u u 1 m 1u 2 m 2 v v 1 n 1v 2 n 2 a 0u 2 i 0 b 0u 2 i 1 0 a 1u 2 i 1 b 1u 2 i 1 1 0 i 0 1 m 1 a 0v 2 j 0 b 0v 2 j 1 0 a 1v 2 j 1 b 1v 2 j 1 1 0 j 0 1 n 1 here f 1 f 2 c 0 1 xr m n r r 0 our hypotheses imposed on the nonlinearities f 1 and f 2 are formulated in terms of nonnegative matrices we use fixed point index theory to establish our main results based on a priori estimates of positive solutions

a monotone iterative technique for solving the bending elastic beam equations abstract this paper discusses the solvability of the fourth order boundary value problem u 4 f t u u 0 t 1 u 0 u 1 u 0 u 1 0 which models a statically bending elastic beam whose two ends are simply supported where f 0 1 r 2 r is continuous we build a maximum principle for the corresponding linear equation using this maximum principle we develop a monotone iterative technique in the presence of lower and upper solutions to solve the nonlinear equation and obtain some existence and uniqueness results

multiple sign changing solutions for fourth order m point boundary value problems abstract in this paper we study the existence and multiplicity of nontrivial solutions for the fourth order m point boundary value problems making use of the theory of the fixed point index in a cone and the leray schauder degree under general conditions on nonlinearity we prove that there exist at least six different nontrivial solutions for the fourth order m point boundary value problems furthermore if the nonlinearity is odd we obtain that there exist at least eight different nontrivial solutions

on fourth order elliptic boundary value problems with nonmonotone nonlinear function this paper is concerned with the fourth order elliptic boundary value problems with nonmonotone nonlinear function the existence and uniqueness of a solution is proven by the method of upper and lower solutions a monotone iteration is developed so that the iteration sequence converges monotonically to a maximal solution or a minimal solution depending on whether the initial iteration is an upper solution or a lower solution

higher order lidstone boundary value problems for elliptic partial differential equations the aim of this paper is to show the existence and uniqueness of a solution for a class of 2nth order elliptic lidstone boundary value problems where the nonlinear functions depend on the higher order derivatives sufficient conditions are given for the existence and uniqueness of a solution it is also shown that there exist two sequences which converge monotonically from above and below respectively to the unique solution the approach to the problem is by the method of upper and lower solutions together with monotone iterative technique for nonquasimonotone functions all the results are directly applicable to 2nth order two point lidstone boundary value problems

a necessary and sufficient condition for the existence of positive solutions of singular super linear m point boundary value problems abstract this paper investigates the existence of positive solutions of singular super linear m point boundary value problems of fourth order ordinary differential equations a necessary and sufficient condition for the existence of c 2 0 1 positive solutions as well as c 3 0 1 positive solutions is given by means of the fixed point theorems on cones

periodic boundary value problem for integrodifferential equations of hammerstein type a general comparison result is developed for first order integrodifferential inequality of hammerstein type with periodic boundary condition it is then used to construct monotone sequences to give out the maximal and minimal solutions of a given pbvp of a first order integrodifferential equation of hammerstein type in which the increasingness of the right hand side function in the argument containing the integral operator is not assumed

the method of lower and upper solutions for fourth order two point boundary value problems abstract in this paper we develop the monotone method in the presence of lower and upper solutions for the problem u iv f x u x u x u 0 u 1 u 0 u 1 0 where f 0 1 r r r is continuous

eigenvalues of fourth order singular sturm liouville boundary value problems abstract in this paper by establishing a new comparison theorem and constructing upper and lower solutions some sufficient conditions of existence of positive solutions for the following nonlinear fourth order singular sturm liouville eigenvalue problem 1 p t p t u t f t u t 0 1 u 0 u 1 0 u 0 lim t 0 p t u t 0 u 1 lim t 1 p t u t 0 are established due to the schauder s fixed point theorem for large enough where 0 0 f and p can be singular at t 0 and or 1 moreover f can also be singular at u 0 in addition some peculiar cases are discussed and some further results are obtained

positive solutions of a 2nth order boundary value problem involving all derivatives via the order reduction method this paper is mainly concerned with the existence multiplicity and uniqueness of positive solutions for the 2nth order boundary value problem 1 nu 2 n f t u u 1 i 2 u i 1 n 1u 2 n 1 u 2 i 0 u 2 i 1 1 0 i 0 1 n 1 where n 2 and f c 0 1 xr 2 n r r 0 we first use the method of order reduction to transform the above problem into an equivalent initial value problem for a first order integro differential equation and then use the fixed point index theory to prove the existence multiplicity and uniqueness of positive solutions for the resulting problem based on a priori estimates achieved by developing spectral properties of associated parameterized linear integral operators finally as a byproduct our main results are applied for establishing the existence multiplicity and uniqueness of symmetric positive solutions for the lidstone problem involving all derivatives

multiple solutions for fourth order boundary value problem abstract in this paper we study the existence and multiplicity of nontrivial solutions for the fourth order two point boundary value problems making use of the theory of fixed point index in cone and leray schauder degree under general conditions on nonlinearity we prove that there exist at least six different nontrivial solutions for the fourth order two point boundary value problems furthermore if the nonlinearity is odd we obtain that there exist at least eight different nontrivial solutions

local existence of multiple positive solutions to a singular cantilever beam equation abstract by constructing suitable cone and control functions we prove some local existence theorems of positive solutions for a singular fourth order two point boundary value problem in mechanics the problem is called cantilever beam equation furthermore we improve a famous method appeared in the studies of singular boundary value problems the approximation theorem of completely continuous operators and the guo krasnosel skii fixed point theorem of cone expansion compression type play important parts in this work

positive solutions of fourth order boundary value problems with two parameters abstract in this paper the existence results of positive solutions are obtained for fourth order boundary value problem u 4 u u f t u 0 where f 0 1 r r is continuous r and satisfy

nontrivial solutions for higher order multi point boundary value problems in the case where a nonlinearity may change sign and contains higher derivatives we consider the existence of nontrivial solutions for a class of higher order multi point boundary value problems some sufficient conditions for the existence of nontrivial solutions are established under certain suitable growth conditions our proof is based on leray schauder nonlinear alternative

solutions of 2nth lidstone boundary value problems and dependence on higher order derivatives abstract in this paper we consider the lidstone boundary value problem 1 n u 2n x f x u x u x u 2 n 1 x 0 u 2i 0 u 2i 1 0 0 i n 1 some monotone conditions are imposed on f which enable us to apply a new maximum principle to deduce the existence of solution the emphasis here is that f depends on higher order derivatives two examples are also included to dwell upon the importance of the results obtained

multiple positive solutions of a m point boundary value problem for 2nth order singular integro differential equations in banach spaces abstract in this paper we obtain the existence of multiple positive solutions of a m point boundary value problem for 2 n th order singular nonlinear integro differential equations in a banach space by means of fixed point index theory of completely continuous operators

error and stability of monotone method for numerical solutions of fourth order semilinear elliptic boundary value problems this paper is concerned with the error and stability analysis of the monotone method for numerical solutions of fourth order semilinear elliptic boundary value problems a comparison result among the various monotone sequences is given the global error is analyzed and some sufficient conditions are formulated to guarantee a geometric rate of convergence the stability of the monotone method is proved some numerical results are presented

positive solutions of fourth order sturm liouville boundary value problems with changing sign nonlinearity abstract in this paper the existence of positive solutions is investigated for the following singular fourth order sturm liouville boundary value problem with changing sign nonlinearity u 4 t a t f t u t u t b t 0 t 1 1 u 0 1 u 0 1 u 1 1 u 1 0 2 u 0 2 u 0 2 u 1 2 u 1 0 where a 0 1 0 is continuous f 0 1 0 0 0 is continuous b 0 1 is lebesgue integrable without any nonnegative assumption on nonlinearity by choosing a proper cone and creating an available integral operator the existence of the positive solutions for the above singular sturm liouville boundary value problem is established some examples are worked out to indicate the application of our main result

upper and lower solution method for fourth order four point boundary value problems this paper is concerned with the fourth order ordinary differential equation u 4 t f t u t u t 0 0 some new existence results are obtained by developing the upper and lower solution method and the monotone iterative technique

multiple positive solutions of a boundary value problem for a class of 2 nth order m point singular integro differential equations in banach spaces in this paper we obtain the existence of multiple positive solutions of a boundary value problem for 2nth order singular nonlinear integro differential equations in a banach space by means of fixed point index theory of completely continuous operators

existence and multiplicity of solutions for fourth order boundary value problems with parameters abstract in this paper we study the existence and multiplicity of the solutions for the fourth order boundary value problem bvp u 4 t u t u t f t u t 0 t 1 u 0 u 1 u 0 u 1 0 where f 0 1 r r is continuous r and r are parameters by means of the idea of the decomposition of operators shown by chen w y chen a decomposition problem for operators xuebao of dongbei renmin university 1 1957 95 98 see also m krasnosel skii topological methods in the theory of nonlinear integral equations gostehizdat moscow 1956 and the critical point theory we obtain that if the pair is on the curve 2 4 satisfying 2 2 then the above bvp has at least one two three and infinitely many solutions for being in different interval respectively

cases of equality in certain multilinear inequalities of hardy riesz rogers brascamp lieb luttinger type abstract cases of equality in certain hardy riesz rogers brascamp lieb luttinger rearrangement inequalities are characterized

a necessary and sufficient condition for 2nth order singular super linear m point boundary value problems abstract in this paper we study the existence of positive solutions for singular super linear m point boundary value problems of 2nth order ordinary differential equations a necessary and sufficient condition for the existence of c 2 n 2 0 1 positive solutions as well as c 2 n 1 0 1 positive solutions is given by means of the fixed point theorems on cones

existence of positive solutions for 2nth order singular superlinear boundary value problems this paper investigates the existence of positive solutions for 2nth order n 1 singular superlinear boundary value problems a necessary and sufficient condition for the existence of c 2 n 2 0 1 as well as c 2 n 1 0 1 positive solutions is given by constructing a special cone and with the e norm

a monotone method for constructing extremal solutions to fourth order periodic boundary value problems in this paper we describe a constructive method which yields two monotone sequences that converge uniformly to extremal solutions to the periodic boundary value problemu 4 t f t u t u t email protected 0 email protected u 0 u email protected u 0 u email protected u 0 u email protected u 0 u email protected in the presence of an upper solution b and a lower solution a with b a

a class of fourth order singular boundary value problems by constructing lower and upper solutions and with the maximal theorem the author gives a necessary and sufficient condition for the existence of c 2 0 1 as well as c 3 0 1 positive solutions of singular boundary value problems for a class of fourth order sublinear differential equations

the method of lower and upper solutions for fourth order singular m point boundary value problems abstract this paper investigates the existence of positive solutions for fourth order singular m point boundary value problems firstly we establish a comparison theorem then we define a partial ordering in c 2 0 1 c 4 0 1 and construct lower and upper solutions to give a necessary and sufficient condition for the existence of c 2 0 1 as well as c 3 0 1 positive solutions our nonlinearity f t x y may be singular at x y t 0 and or t 1

positive solutions for a class of boundary value problems with integral boundary conditions this paper investigates the existence and multiplicity of positive solutions for a class of nonlinear boundary value problems of fourth order differential equations with integral boundary conditions the arguments are based upon a specially constructed cone and the fixed point theory in cone the nonexistence of positive solutions is also studied

a class of 2nth order singular boundary value problems abstract this paper investigates the existence of positive solutions for 2 n th order n 1 singular sub linear boundary value problems first of all we establish the maximal principle and some important lemmas then we define a partial ordering in c 2 n 2 0 1 c 2 n 0 1 and construct lower and upper solutions to give a necessary and sufficient condition for the existence of c 2 n 2 0 1 as well as c 2 n 1 0 1 positive solutions our nonlinearity f t x 1 x 2 x n may be singular at x i 0 i 1 2 n t 0 and or t 1

searching the least value method for solving fourth order nonlinear boundary value problems this paper obtains a searching least value slv method for a class of fourth order nonlinear boundary value problems is investigated the argument is based on the reproducing kernel space w 5 0 1 the approximate solutions u n x and u n k x are uniformly convergent to the exact solution u x and u k x k 1 2 3 4 respectively numerical results are verified that the method is quite accurate and efficient for this kind of problem

boundary value problems for nonlinear impulsive integrodifferential equations we consider boundary value problems for nonlinear impulsive integrodifferential equations in which impulses occur at fixed times by suitably modifying the notions of upper and lower solutions we establish existence results in a sector then develop the monotone method and prove the existence of extremal solutions of the impulsive integrodifferential equations as an application we derive some existence results for a boundary value problem for a third order impulsive differential equation

positive solutions for 2nth order singular sub linear m point boundary value problems abstract this paper investigates the existence of positive solutions for 2nth order singular sub linear m point boundary value problems firstly we establish a comparison theorem then we define a partial ordering in c2n 2 a b c2n a b and construct lower and upper solutions to give a necessary and sufficient condition for the existence of c2n 2 0 1 as well as c2n 1 0 1 positive solutions our nonlinearity f t x1 x2 xn may be singular at xi 0 i 1 2 n t 0 and or t 1

existence and uniqueness of solutions for a fourth order boundary value problem abstract in this paper we study the fourth order two point boundary value problem x t f t x t x t x t x t 0 t 0 1 x 0 x 1 0 a x 0 b x 0 0 c x 1 d x 1 0 by means of lower and upper solution method growth conditions on the nonlinear term f which guarantee the existence of solutions for the above boundary value problem are given in particular we obtain the uniqueness of the solution by imposing a monotone condition of the term f

positive solutions of fourth order nonlinear singular sturm liouville eigenvalue problems abstract we consider the existence of positive solutions for the following fourth order singular sturm liouville eigenvalue problems 1 p t p t u t g t f t u u 0 0 t 1 1 u 0 1 u 0 0 1 u 1 1 u 1 0 2 u 0 2 lim t 0 p t u t 0 2 u 1 2 lim t 1 p t u t 0 where 0 g p may be singular at t 0 and or 1 moreover f t x y may also have singularity at x 0 and or y 0 by using fixed point theory in cones an explicit interval for is derived such that for any in this interval the existence of at least one positive solution to the boundary value problem is guaranteed our results extend and improve many known results including singular and nonsingular cases

on 2nth order lidstone boundary value problems this paper is concerned with the solutions of a class of 2nth order lidstone boundary value problems sufficient conditions for the existence and uniqueness of a solution are given a monotone iteration is developed so that the iteration sequence converges monotonically to a maximal or a minimal solution the approach to the problem is by the method of upper and lower solutions with a new maximum principle

a fourth order compact finite difference method for higher order lidstone boundary value problems a compact finite difference method is proposed for a general class of 2nth order lidstone boundary value problems the existence and uniqueness of the finite difference solution is investigated by the method of upper and lower solutions without any monotone requirement on the nonlinear term a monotone iteration process is provided for solving the resulting discrete system efficiently and a simple and easily verified condition is obtained to guarantee a geometric convergence of the iterations the convergence of the finite difference solution and the fourth order accuracy of the proposed method are proved numerical results demonstrate the high efficiency and advantages of this new approach

existence and uniqueness of positive solutions for a higher order boundary value problem the goal of this paper is to study the existence and uniqueness of positive solutions for the 2nth order boundary value problem 1 nu 2 n f t u u 1 n 1u 2 n 2 a 0u 2 i 0 email protected 0u 2 i 1 0 0 i 0 1 n 1 a 1u 2 i 1 email protected 1u 2 i 1 1 0 i 0 1 n 1 the krein rutman theorem and the krasnoselskii zabreiko fixed point theorem are the main tools that have been used to develop our work

multiply sign changing solutions for fourth order nonlinear boundary value problems abstract this paper deals with the existence of sign changing solutions for the fourth order nonlinear boundary value problem u 4 f u u 0 t 1 u 0 u 1 u 0 u 1 0 where f r 2 r is a continuously odd function some conditions on f guaranteeing the existence and multiplicity of sign changing solutions are presented the existence and multiplicity conditions concern the eigenline of the associated two parameter linear eigenvalue problem the discussion is based on the fixed point index theory in cones and an anti symmetrical extension method of solution

the method of lower and upper solutions for a bending of an elastic beam equation abstract in this paper by combining a new maximum principle and the theory of the two parameter linear eigenvalue problem we develop the monotone method in the presence of lower and upper solutions for the problem u 4 x f x u x u x 0 x 1 u 0 u 1 u 0 u 1 0 where f 0 1 r r r is continuous

two parameter nonresonance condition for the existence of fourth order boundary value problems abstract in this paper we discuss the existence of the fourth order boundary value problem u 4 f t u u 0 t 1 u 0 u 1 u 0 u 1 0 where f 0 1 r r r is continuous and partly solve the del pino and manasevich s conjecture on the nonresonance condition involving the two parameter linear eigenvalue problem we also present a two parameter nonresonance condition described by circle

periodic boundary value problems for integro differential equations of volterra type on etudie l existence des solutions pour un probleme aux valeurs limites periodique pour l equation integrodifferentielle u f t u tu u 0 u 2 f c 0 2 r r r tu t 0 t k t s u s ds et k c 0 2 0 2 r

existence of solutions for 2n order boundary value problem in this paper we discuss the existence of solutions for the 2n order boundary value problem 1 nu 2 n t f t u t u t u 2 n 2 t 0r is continuous

fourth order compact finite difference method for fourth order nonlinear elliptic boundary value problems a compact finite difference method with non isotropic mesh is proposed for a two dimensional fourth order nonlinear elliptic boundary value problem the existence and uniqueness of its solutions are investigated by the method of upper and lower solutions without any requirement of the monotonicity of the nonlinear term three monotone and convergent iterations are provided for resolving the resulting discrete systems efficiently the convergence and the fourth order accuracy of the proposed method are proved numerical results demonstrate the high efficiency and advantages of this new approach

existence of n solutions and or positive solutions to a semipositone elastic beam equation abstract the existence of n solutions and or positive solutions is established for a nonlinear fourth order two point boundary value problem where n is an arbitrary natural number and the nonlinear term has a nonpositive lower bound in mechanics the problem describes deformation of the elastic beam whose two ends are simply supported the main results show that the problem has at least n solutions and or positive solutions provided that the heights of the nonlinear term are appropriate on some bounded sets

second and higher order systems of boundary value problems abstract existence results for systems of kth order boundary value problems are presented our analysis is based on a nonlinear alternative of a granas and use of a priori bounds

existence of a positive solution of a fourth order boundary value problem abstract in this paper the existence of a positive solution of the boundary value problem of the following fourth order nonlinear differential equation x 4 f t x x x 0 x 0 x t x t 0 is discussed

positive solutions of fourth order two point boundary value problems in this paper by using the krasnoselskii fixed point theorem we study the existence of one or multiple positive solution of the fourth order two point boundary value problem y 4 t f t y t y t y 0 y 1 y 0 y 1 0 we also give some examples to illustrate our results

eigenvalue of fourth order m point boundary value problem with derivatives this paper deals with the existence of positive solutions for the fourth order nonlinear ordinary differential equation x t lg t f t x t x t 0 0 are constants such that r a d a c b d 0 and x i 0 1 h i 0 i 1 2 m 2 by means of a fixed point theorem due to krasnaselskii some new existence results of positive solutions for the above multi point boundary value problem are obtained which improve the main results of graef et al j r graef c qian b yang a three point boundary value problem for nonlinear fourth order differential equations j math anal appl 287 2003 217 233 an example is given to demonstrate the main results of this paper

extremal optimization of graph partitioning at the percolation threshold the benefits of a recently proposed method to approximate hard optimization problems are demonstrated on the graph partitioning problem the performance of this new method called extremal optimization eo is compared with simulated annealing sa in extensive numerical simulations while generally a complex np hard problem the optimization of the graph partitions is particularly difficult for sparse graphs with average connectivities near the percolation threshold at this threshold the relative error of sa for large graphs is found to diverge relative to eo at equalized runtime on the other hand eo based on the extremal dynamics of self organized critical systems reproduces known results about optimal partitions at this critical point quite well