the existence of countably many positive solutions for singular multipoint boundary value problems abstract in this paper we study the existence of countably many positive solutions for a singular multipoint boundary value problem by using fixed point index theory and the leggett williams fixed point theorem sufficient conditions for the existence of countably many positive solutions are established

existence of positive solutions for fourth order m point boundary value problem with variable parameters in this paper we investigate the existence of positive solutions for a class of nonlinear fourth order m point boundary value problem with two variable parameters by using the fixed point index theory we give some new existence results

positive solutions of some singular m point boundary value problems at non resonance this paper investigates the existence of positive solutions for second order singular m point boundary value problems at non resonance a necessary and sufficient condition for the existence of c 0 1 as well as c 1 0 1 positive solutions is given by constructing lower and upper solutions and with the maximal theorem our nonlinearity f t x may be singular at x t 0 and or t 1

twin positive solutions for higher order m point boundary value problems with sign changing nonlinearities a new fixed point theorem on double cones is applied to obtain the existence of at least two positive solutions for the 2nd order m point boundary value problemy 2 n t f t y t y t y 2 n 1 t 0

multiple positive solutions for multipoint boundary value problems with one dimensional p laplacian abstract in this paper we consider the multiplicity of positive solutions for the one dimensional p laplacian differential equation p u q t f t u u 0 t 0 1 subject to some boundary conditions by means of a fixed point theorem due to avery and peterson we provide sufficient conditions for the existence of multiple positive solutions to some multipoint boundary value problems

some model theory over hereditary noetherian domains questions in the model theory of modules over hereditary noetherian domains are investigated with particular attention being paid to differential polynomial rings and to generalized weyl algebras we prove that there exists no isolated point in the ziegler spectrum over a simple hereditary generalized weyl algebra a of the sort considered by bavula algebra i analiz 4 1 1992 75 97 over a field k with char k 0 the first weyl algebra a 1 k is one such and the category of finite length modules over a does not have any almost split sequence we show that the theory of all modules over a wide class of generalized weyl algebras and related rings interprets the word problem for groups and in the case that the field is countable there exists a superdecomposable pure injective module over a this class includes for example the universal enveloping algebra usl 2 k

existence of multiple positive solutions for nonlinear m point boundary value problems in this paper we afford some sufficient conditions to guarantee the existence of multiple positive solutions for the nonlinear m point boundary value problem for the one dimensional p laplacian f p u f t u 0 t 0 1 u 0 i 1m 2b iu x i u 1 i 1m 2a iu x i

k theory and right ideal class groups for hnp rings let r be an hereditary noetherian prime ring let s be a dedekind closure of r and let r be the category of finitely generated s torsion r modules it is shown that for all i 0 there is an exact sequence 0 ki t ki r ki s o if i 0 or r has finitely many idempotent ideals then this sequence splits a notion of right ideal class group is then introduced for hereditary noetherian prime rings which generalizes the standard definition of class group for hereditary orders over dedekind domains it is shown that there is a decomposition o r cl r ffl f where f is a ree abelian group whose ra k depends on the number of idempotent maximal ideals of r moreover there is a natural is morphism cl r cl s and this decomposition corresponds closely to the splitting of the above exact sequence for ko

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

positive solutions to a new kind sturm liouville like four point boundary value problem abstract in this paper we considered the following four point boundary value problem x t h t f t x t x t 0 0 t 1 x 0 1 x 0 x 1 2 x 0 where 0 1 1 0 2 1 1 0 1 1 2 1 2 1 2 0 by applying fixed point theorems we obtain a variety of existence results in particular our four point boundary condition is a new kind sturm liouville like boundary condition which has rarely been considered up to now

existence of nonnegative solutions for second order m point boundary value problems at resonance abstract in this paper the minimal and maximal nonnegative solutions for second order m point boundary value problems at resonance are investigated by using a new fixed point theorem of increasing operators and the monotone iterative sequences which converge to solutions are given the method is different essentially from the previous papers used by coincidence degree continuation theorem of mawhin

a generalized multi point boundary value problem for second order ordinary differential equations let f 0 1 x r 2 r be a function satisfying caratheodory s conditions and e t l 1 0 1 let x i t j 0 1 a i b j r i 1 2 m 2 j 1 2 n 2 0 x 1 x 2 x m 2 1 0 t 1 t 2 t n 2 1 be given this paper is concerned with the problem of existence of a solution for the generalized multi point boundary value problems x t f t x t x t e t 0

multiplicity results for a three point boundary value problem at resonance this paper deals with second order three point boundary value problem u t f t u t t 0 1 u 0 0 u 1 u where f 0 1 r r is continuous 0 and 0 1 are given constants such that 1 we develop the methods of lower and upper solutions by the connectivity properties of the solution set of parameterized families of compact vector fields as applications of these methods we get several multiplicity results for the problems under consideration

nontrivial solutions of singular nonlinear m point boundary value problems in this paper by using the method of topology degree some existence theorems of nontrivial solutions for singular nonlinear m point boundary value problems are established our nonlinearity may be singular in its dependent variable

existence and iteration of positive solutions to a class of sturm liouville like p laplacian boundary value problems abstract this paper deals with the existence and iteration of positive solutions for the following p laplacian differential equation p u t q t f t u t u t 0 t 0 1 subject to the following sturm liouville like four point boundary condition u 0 u 0 u 1 u 0 where 0 1 by applying the monotone iterative technique and without the assumption of the existence of lower and upper solutions we not only obtain the existence of positive solutions for the problems but also establish iterative schemes for approximating the solutions

higher order m point boundary value problems on time scales in this paper we investigate the existence of positive solutions for nonlinear even order m point boundary value problems on time scales by means of fixed point theorems

existence of positive solutions for three point boundary value problems at resonance with the help of the theorem of a fixed point index for a proper semilinear operators established by cremins we get a existence theorem concerning the existence of positive solution for the second order ordinary differential equation of three point boundary value problems at resonance

positive solution of singular higher order m point boundary value problem with nonlinearity that changes sign this paper is about a class of singular higher order m point boundary value problems with nonlinearity that changes sign using the fixed point index theory we get a sufficient condition for the existence of positive solution to this problem

existence and nonexistence of positive solutions for a class of nth order three point boundary value problems in banach spaces by using the fixed point principle in cone and the fixed point index theory for strict set contraction operator this paper investigates the existence nonexistence and multiplicity of positive solutions for a class of nonlinear three point boundary value problems of nth order differential equations in ordered banach spaces in addition an example is included to demonstrate the main results

multiple positive solutions of multi point boundary value problem for second order impulsive differential equations this paper is devoted to study the existence of multiple positive solutions for the second order multi point boundary value problem with impulse effects the arguments are based upon fixed point theorems in a cone an example is worked out to demonstrate the main results

existence and iteration of monotone positive solutions for multipoint boundary value problem with p laplacian operator in the paper we obtain the existence of monotone positive solutions and establish acorresponding iterative scheme for the following multipoint boundary value problem with p laplacian operator f p u t q t f t u t 0 0

model order reduction for parametrized nonlinear hyperbolic problems as an application to uncertainty quantification abstract in this work we present a model order reduction mor technique for hyperbolic conservation laws with applications in uncertainty quantification uq the problem consists of a parametrized time dependent hyperbolic system of equations where the parameters affect the initial conditions and the fluxes in a non linear way the procedure utilized to reduce the order is a combination of a greedy algorithm in the parameter space a proper orthogonal decomposition pod in time and empirical interpolation method eim to deal with non linearities drohmann 2012 we provide under some hypothesis an error bound for the reduced solution with respect to the high order one the algorithm shows small errors and savings of the computational time up to 90 in the uq simulations which are performed to validate the algorithm

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

three point boundary value problems for difference equations in this paper the existence and nonexistence of positive solutions for three point nonlinear boundary value problems of difference equations are considered

wild torsion modules over weyl algebras and general torsion modules over hnps let a 1 be the first weyl algebra over a field f of characteristic zero we show that the category of a 1 modules of finite length is wild despite the fact that every a 1 module of finite length is cyclic in fact the category of a 1 modules not necessarily finitely generated of socle height 2 is wild in a very strong sense among the applications we show i essentially any f algebra can occur as the endomorphism algebra of an a 1 module of socle height 2 ii a 1 has very large indecomposable modules of finite length iii there is an hnp hereditary noetherian prime ring that has indecomposable modules of finite length requiring arbitrary many generators we also complete the basic theory of finitely generated modules over general hnps by showing that every such module is a direct sum of right ideals and homomorphic images of right ideals and by proving a simultaneous decomposition theorem for an arbitrary projective module and submodule

existence of triple positive solutions for multi point boundary value problems with a one dimensional p laplacian in this paper we consider the existence of multiple positive solutions for multi point boundary value problems with a one dimensional p laplacian f p u t q t f t u t u t 0 01 a email protected email protected i email protected email protected m 2 0 i 1 m email protected i i 1 m email protected email protected 0 1 0 x 1 x 2 x m 2 1 by the fixed point theorem due to avery and peterson we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem

positive solutions for multipoint boundary value problems with a one dimensional p laplacian abstract in this paper we consider the multipoint boundary value problem for a one dimensional p laplacian p u f t u 0 t 0 1 subject to the boundary value condition u 0 i 1 n 2 i u i u 1 i 1 n 2 i u i where p s s p 2 s p 1 i 0 1 with 0 1 2 n 2 1 and i i satisfy i i 0 0 i 1 n 2 i 1 and i 1 n 2 i 1 using a fixed point theorem for operators on a cone we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem

positive solutions for a class of boundary value problem with integral boundary conditions in banach spaces this paper investigates the existence and multiplicity of positive solutions for a class of nonlinear boundary value problem of second order differential equations with integral boundary conditions in ordered banach spaces the arguments are based upon a specially constructed cone and the fixed point theory in a cone for strict set contraction operators the nonexistence of a positive solution is also studied

existence of multiple positive solutions for m point boundary value problems in banach spaces this paper deals with the positive solutions of m point nonlinear boundary value problem in banach spaces by using the fixed point theorem of strict set contractions some sufficient conditions for the existence of at least one or two positive solutions to m point boundary value problem in banach spaces are obtained an example illustrating the main results is given

successive iteration and positive solutions for a third order multipoint generalized right focal boundary value problem with p laplacian abstract in this paper we study the existence of positive solutions for the one dimensional p laplacian differential equation p u t q t f t u t u t u t 0 t 1 subject to the following multipoint generalized right focal boundary condition u 0 i 1 m i u i u 0 u 1 i 1 n i u i by applying a monotone iterative method we not only obtain the existence of positive solutions for the problem but also establish iterative schemes for approximating the solutions

multiple positive solutions for nonlinear m point boundary value problems in this paper we consider the existence and multiplicity of positive solutions for the m boundary value problems p t u q t u f t u 0 0

positive solutions of m point boundary value problems for higher order ordinary differential equations abstract in this paper we study m point boundary value problems for higher order ordinary differential equation y 2 n t f t y t y t y 2 n 1 t 0 t 1 y 2 i 0 0 y 2 i 1 j 1 m 2 k i j y 2 i j 0 i n 1 where f is allowed to change sign and 0 0 1 2 m 2 m 1 1 we show sufficient conditions for the existence of at least two positive solutions by applying a new fixed point theorem in cones and the associated green s function in particular the second positive solutions for the above problem is not concave

on numerical studies of multi point boundary value problem and its fold bifurcation based upon shooting method we set up a numerical method for approximating solutions and fold bifurcation solutions of second order multi point boundary value problems we prove the equivalence of the regularity of solutions and simple fold bifurcation solutions between the numerical method and the multi point boundary value problems many numerical experiments are carried out to illustrate the theoretical analysis from which we explore that the fold bifurcation phenomenon are generic in multi point boundary value problems although there is no theoretical analysis in the literature so far

successive iteration and positive symmetric solution for a sturm liouville like four point boundary value problem with a p laplacian operator abstract in this paper we consider the following sturm liouville like four point p laplacian boundary value problem with the nonlinear term f depending on the first order derivative p u t q t f t u t u t 0 0 t 1 subject to the boundary conditions u 0 u 0 u 1 u 0 by using a monotone iterative technique the existence of symmetric positive solutions and corresponding iterative schemes are obtained

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

a symmetric solution of a multipoint boundary value problem with one dimensional p laplacian at resonance abstract we apply an extension of mawhin s continuation theorem due to ge to show the existence of at least one symmetric solution of the multipoint boundary value problem for the one dimensional p laplacian at resonance p x t f t x t x t t 0 1 subject to the boundary conditions x 0 i 1 n i x i x 1 i 1 n i x i where p s s p 2 s p 1 0 1 2 n 1 2 i i 1 i 1 2 n i 1 n i 1 f 0 1 r 2 r with f t u v f 1 t u v for t u v 0 1 r 2 satisfying the caratheodory conditions

symmetric positive solutions of boundary value problems with integral boundary conditions under conditions weaker than those used by ma we establish various results on the existence and nonexistence of symmetric positive solutions to fourth order boundary value problems with integral boundary conditions the arguments are based upon a specially constructed cone and the fixed point theory in a cone our results improve and extend that obtained in h ma symmetric positive solutions for nonlocal boundary value problems of fourth order nonlinear anal 68 2008 645 651 we illustrate our results by one example which cannot be handled using the existing results

successive iteration and positive symmetric solutions for some sturm liouville like four point p laplacian boundary value problems this paper deals with the existence of positive solutions for some sturm liouville like four point p laplacian boundary value problems our approach is based on the fixed point theorem and the monotone iterative technique without the assumption of the existence of lower and upper solution we obtain not only the existence of positive solutions for the problems but also establish iterative schemes for approximating the solutions

multiplicity of symmetric positive solutions for a multipoint boundary value problem with a one dimensional p laplacian abstract in this paper we consider the multipoint boundary value problem for the one dimensional p laplacian p u t q t f t u t u t 0 t 0 1 subject to the boundary conditions u 0 i 1 n i u i u 1 i 1 n i u i where p s s p 2 s p 1 i 0 0 i 1 n i 1 0 1 2 n 1 2 i i 1 i 1 2 n applying a fixed point theorem of functional type in a cone we study the existence of at least three symmetric positive solutions to the above boundary value problem the interesting point is that the nonlinear term f contains the first order derivative explicitly

three positive solutions for higher order m point boundary value problems abstract in this paper we consider the existence of at least three positive solutions for the 2nth order m point boundary value problem y 2n t f t y t y t y 2 n 1 t 0 t 1 y 2i 0 0 y 2i 1 j 1 m 2 k ij y 2i j 0 i n 1 where kij 0 i 0 1 n 1 j 1 2 m 2 0

existence of positive solution for singular semi positone k n k conjugate m point boundary value problem this paper is about a class of singular semi positone k n k conjugate m point boundary value problems by using the fixed point index theory we get a sufficient condition for the existence of positive solution to this problem

existence of three positive solutions for m point boundary value problems with one dimensional p laplacian abstract in this paper we consider the multipoint boundary value problem for the one dimensional p laplacian p u q t f t u t u t 0 t 0 1 subject to the boundary conditions u 0 0 u 1 i 1 m 2 a i u i where p s s p 2 s p 1 i 0 1 with 0 1 2 m 2 1 and a i 0 1 0 i 1 m 2 a i 1 using a fixed point theorem due to avery and peterson we study the existence of at least three positive solutions to the above boundary value problem the interesting point is that the nonlinear term f explicitly involves a first order derivative

a necessary and sufficient condition for the existence of positive solutions to singular sublinear three point boundary value problems abstract this paper investigates the existence of positive solutions for second order singular sublinear three point boundary value problems a necessary and sufficient condition for the existence of c 0 1 as well as c 1 0 1 positive solutions is given by constructing lower and upper solutions and with the maximal theorem also the uniqueness iterative methods convergence rate and computational methods of the c 1 0 1 positive solutions are studied our nonlinear term may be singular at t 0 and or t 1

positive solutions of a general discrete boundary value problem in this paper the existence of positive solutions for a nonlinear general discrete boundary value problem is established such results extend and improve some known facts for the two point and three point boundary value problems particularly the boundary value conditions can be nonlinear and the method is new for explaining the main results some numerical examples are also given

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

multiple positive solutions for multipoint boundary value problems with sign changing nonlinearity abstract in this paper we consider the multipoint boundary value problem for one dimensional p laplacian p u q t f t u 0 t 0 1 subject to the boundary value conditions u 0 i 1 n i u i u 1 i 1 n i u i where p s s p 2s p 1 i 0 1 with 0 1 2 n 1 and i i 0 satisfy 0 i 1 n i i 1 n i 1 the nonlinear term f may change sign using a fixed point theorem for operators in a cone we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem

positive solutions to a generalized second order three point boundary value problem abstract in this paper by using krasnoselskii fixed point theorem we study the existence of at least or two positive solutions to the nonlinear second order three point boundary value problem y t a t f y t 0 0 t t y 0 y y t y where 0 t 0 t 0 t t are given constants as an application we also give some examples to demonstrate our results

hereditary noetherian prime rings 2 finitely generated projective modules abstract let r be a hereditary noetherian prime ring we determine a full set of invariants for the isomorphism class of any finitely generated projective r module of uniform dimension at least 2 in particular we prove that p x q x implies p q whenever p has uniform dimension at least 2 among the applications of these results are necessary and sufficient conditions for the existence of a bound to the number of generators needed for right ideals of r

positive solutions for second order m point boundary value problems by using the schauder fixed point theorem and analysis method we establish the existence of solutions for the m point boundary value problem u t a t f u 0 u 0 0 u 1 i 1m 2kiu i b where b ki 0 i 1 2 m 2 0 b

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 of two solutions of m point boundary value problem for second order dynamic equations on time scales in this paper by means of a new twin fixed point theorem in a cone the existence of at least two positive solutions of m point boundary value problem for second order dynamic equations on time scales is considered

positive solutions of a second order integral boundary value problem in this paper we study the existence of positive solutions of a second order integral boundary value problems for ordinary differential equations our results presented here unify generalize and substantially improve the existing results in the literature moreover it is worthwhile to point out that our method will dispense with constructing a new green function

solvability of an m point boundary value problem for second order ordinary differential equations let 0 1 r2 r be a function satisfying caratheodory s conditions and e t l1 0 1 let i 0 1 ai r all of the ai s having the same sign i 1 2 m 2 0 1 2 m 2 1 be given this paper is concerned with the problem of existence of a solution for the m point boundary value problem x t t x t x t e t t 0 1 e formula conditions for the existence of a solution for the above boundary value problem are given using the leray schauder continuation theorem

positive solutions for nonlinear m point eigenvalue problems in this paper we are concerned with determining values of lambda for which there exist positive solutions of the nonlinear eigenvalue problem graphics where a b c d is an element of 0 infinity xi i is an element of 0 1 alpha i beta i is an element of 0 infinity for i is an element of 1 m 2 are given constants p q is an element of c 0 1 0 infinity h is an element of c 0 1 0 infinity and f is an element of c 0 infinity 0 infinity satisfying some suitable conditions our proofs are based on guo krasnoselskii fixed point theorem c 2004 elsevier inc all rights reserved

triple positive solutions for nonlinear boundary value problems in banach space in this paper by applying two pairs of lower and upper solutions method and the topological degree theory of strict set contractions the existence of at least three positive solutions to m point boundary value problems for second order ordinary differential equations in banach spaces is obtained

multiple positive solutions for second order m point boundary value problems abstract in this paper the second order m point boundary value problem u t f t u 0 0 t 1 u 0 0 u 1 i 1 m 2 k i u i 0 is studied where k i 0 i 1 2 m 2 0 1 2 m 2 1 we give at first the associated green s function and its properties for the m point boundary value problem and growth conditions are imposed on f which yield the existence of at least three positive solutions by using the five functionals fixed point theorem and the properties

existence of multiple positive solutions for one dimensional p laplacian abstract in this paper we consider the multipoint boundary value problem for one dimensional p laplacian p u f t u 0 t 0 1 subject to the boundary value conditions p u 0 i 1 n 2 a i p u i u 1 i 1 n 2 b i u i where p s s p 2 s p 1 i 0 1 with 0 1 2 n 2 1 and a i b i satisfy a i b i 0 0 i 1 n 2 a i 1 and i 1 n 2 b i 1 using a fixed point theorem for operators on a cone we provide sufficient conditions for the existence of multiple at least three positive solutions to the above boundary value problem

on an m point boundary value problem for second order ordinary differential equations where q e 0 1 is given we obtain conditions for the existence and uniqueness of a solution for the boundary value problem 2 using the leray schauder continuation theorem 2 we give an example of a three point boundary value problem where the existence condition is not satisfied and no solution exists gupta 3 recently studied the boundary value problem 2 when q 1 our results on the three point boundary value problem 2 extend the results of gupta 3 to the case of general cy see also 4 51 we use the classical spaces c o 11 c o 11 lk o 11 and l o l of continuous k times continuously differentiable measurable real valued functions whose kth power of the absolute value is lebesgue integrable on 0 11 or measurable functions that are essentially bounded

optimal control of parameter dependent convection diffusion problems around rigid bodies this paper is concerned with optimal control problems of elliptic partial differential equations in particular parametrized convection diffusion problems are considered where the parameter appears in the coefficients of the partial differential equation moreover the presence of one or more rigid bodies is assumed inside the domain both the theory existence differentiability optimality criteria is investigated and the numerical solution projected gradient scheme of such problems is carried out finally it is shown that optimizing the efficiency of a rotating propeller fits into the presented framework and the results of corresponding numerical experiments are given

existence of multiple positive solutions for multipoint boundary value problems with a one dimensional p laplacian abstract in this paper we consider the multipoint boundary value problem for a one dimensional p laplacian p u a t f t u 0 t 0 1 u 0 0 u 1 i 1 m 2 a i u i where p s s p 2 s p 1 0 1 2 m 2 1 a i 0 for i 1 2 m 3 and a m 2 0 using a fixed point theorem for operators on a cone we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem

a variational approach for estimating the compliance of the cardiovascular tissue an inverse fluid structure interaction problem estimation of the stiffness of a biological soft tissue is useful for the detection of pathologies such as tumors or atherosclerotic plaques elastography is a method based on the comparison between two images before and after a forced deformation of the tissue of interest an inverse elasticity problem is then solved for young s modulus estimation in the case of arteries no forced deformation is required since vessels naturally move under the action of blood young s modulus can therefore be estimated by solving a coupled inverse fluid structure interaction problem in this paper we focus on the mathematical properties of this problem and its numerical solution we give some well posedness analysis and some preliminary results based on a synthetic data set i e test cases where the exact young s modulus is known and the displacement dataset is numerically generated by solving a forward fluid structure interaction problem we address the problem of the presence of the noise in the measured displacement and of the proper sampling frequency for obtaining reliable estimates

loss of positivity in a nonlinear second order ordinary differential equations we consider existence of nonzero solutions to the following boundary value problem u t f t u 0 t 0 1 u 0 u u 1 u 0 where and are positive parameters 0 1 we prove that solutions lose positivity as the parameter or increases in particular we study problems where the associated integral equation has a kernel that changes sign the proof is based on the fixed point theorem in cones

three positive solutions for second order m point boundary value problems for the second order m point boundary value problemu t f t u 0 0 0 i 1 2 m 2 0 x 1 x 2 x m 2 1 growth conditions are imposed on f which yield the existence of at least three positive solutions by using the leggett williams fixed point theorem the associated green s function for the m point boundary value problem is also given

existence and iteration of positive solutions for a generalized right focal boundary value problem with p laplacian operator abstract in the paper we obtain the existence of positive solutions and establish a corresponding iterative scheme for the following third order generalized right focal boundary value problem with p laplacian operator p u t q t f t u t 0 t 1 u 0 i 1 m i u i u 0 u 1 i 1 n i u i the main tool is the monotone iterative technique

existence of multiple positive solutions for nonlinear m point boundary value problems abstract in this paper we afford some sufficient conditions to guarantee the existence of multiple positive solutions for the nonlinear m point boundary value problem for the one dimensional p laplacian p u a t f t u 0 t 0 1 u 0 0 u 1 i 1 m 2 a i u i

positive solutions of singular three point boundary value problems for second order differential equations in this paper we study the existence of positive solutions of a singular three point boundary value problem for the following second order differential equation y ma t f t y t 0 t 0 1 y 0 by 0 0 y 1 ay h where m 0 is a parameter b 0 0 0 by constructing an available integral operator and combining fixed point index theory with properties of green s function under some conditions concerning the first eigenvalues corresponding to the relevant linear operator the sufficient conditions of the existence of positive solutions for the boundary value problems are established the interesting point of the results is that the term a t may be singular at t 0 and or t 1 moreover the nonlinear f t x is also allowed to have singularity at x 0

positive solutions of m point boundary value problems the second order m point boundary value problem x h x f x 0 0 x 1 0 0 1 i 1m 2ai i is considered under some conditions concerning the first eigenvalue of the relevant linear operator where i 0 1 with 0 1 2 m 2 1 ai 0 with i 1m 2ai 1 h x is allowed to be singular at x 0 and x 1 the existence of positive solutions and multiple positive solutions is obtained by means of fixed point index theory similarly conclusions hold for some other m point boundary value conditions

existence results for nonlinear boundary value problems with integral boundary conditions in banach spaces abstract this paper investigates the multiplicity of positive solutions for a class of nonlinear boundary value problems of fourth order differential equations with integral boundary conditions in ordered banach spaces the arguments are based upon a specially constructed cone and the fixed point index theory in cone for strict set contraction operator the nonexistence of positive solution is also studied meanwhile an example is worked out to demonstrate the main 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

positive solutions for singular m point boundary value problems with positive parameter in this paper some new existence results for positive solutions for a class of singular m point boundary value problems with parameter be obtained

monotone positive solutions of second order multi point boundary value problems abstract in this paper by using guo krasnosel skii fixed point theorem and schauder s fixed point theorem we establish sufficient conditions for the existence and nonexistence of monotone increasing positive solution for a class of second order differential equation with multi point nonhomogeneous boundary conditions