on the method of tangent hyperbolas on banach spaces abstract as an application of the technique employed by the author in a series of papers 15 18 some results are established concerning convergence of the method of tangent hyperbolas for solving nonlinear equations in banach spaces as well as existence and uniqueness of solution the results are compared with those obtained by doring 5

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

three positive solutions for a generalized laplacian boundary value problem with a parameter concerned is a generalized laplacian boundary value problem with a positive parameter first we apply the leggett williams fixed point theorem to establish sufficient conditions on the existence of at least three positive solutions for the parameter belonging to an explicit interval then under a little bit stronger assumptions we show that there are at least three positive symmetric solutions for the parameter in an open interval the obtained results are new even for laplacian boundary value problems and they are illustrated with an example

eigenvalue intervals for a two point boundary value problem on a measure chain we study the existence of eigenvalue intervals for the second order differential equation on a measure chain x t p t f x t 0 t t1 t2 satisfying the boundary conditions x t1 x t1 0 and x t2 x t2 0 where f is a positive function and p a nonnegative function that is allowed to vanish on some subintervals of t1 t2 of the measure chain the methods involve applications of a fixed point theorem for operators on a cone in a banach space

application of iterative processes of r order at least three to operators with unbounded second derivative abstract in this paper we apply a family of newton like methods which contains the best known iterative processes to operator equations where the usual convergence conditions are relaxed we weaken these conditions by assuming f x0 and f x f y x y with a non decreasing continuous real function our results include the ones obtained when the convergence of the family is studied under lipschitz continuous or holder continuous conditions for the second derivative of the operator involved to finish we apply the study to boundary value problems

on the existence and nonexistence of positive solutions for nonlinear sturm liouville boundary value problems abstract in this paper the existence and nonexistence results of positive solutions are obtained for sturm liouville boundary value problem p x u q x u f x u x 0 1 a u 0 b p 0 u 0 0 c u 1 d p 1 u 1 0 where p c 1 0 1 q c 0 1 p x 0 q x 0 for x 0 1 f c 0 1 r a b c d 0 are constants and satisfy a b c d 0 the discussion is based on the positivity estimation for the green s function of associated linear boundary value problem and the fixed point index theory in cones

positive solutions of two point boundary value problems for second order differential equations with the nonlinearity dependent on the derivative abstract the existence of positive solutions is established for two point boundary value problems for second order differential equations with the nonlinearity dependent on the derivative l x h x f x x 0 x 1 r 1 1 0 1 0 0 r 2 2 1 2 1 0 where l x p x x q x x conditions are given in terms of the relative behaviors of the quotient f u v u v for u v near 0 and

on the error estimates of several newton like methods1partial supported by the national natural science foundation of china and by natural science foundation of zhejiang province 1 in this paper convergence theorems and error estimates for several newton like iteration methods under new kantorovitch ostrowski type conditions using the information of higher derivatives at initial point s are established we get not only the convergence speed estimates of iterative sequence x n but also the estimates of f x n 1 f x n

eigenvalue problems for nonlinear differential equations on a measure chain abstract values of are determined for which there exist positive solutions of the second order differential equation on a measure chain u t a t f u t 0 t 0 1 satisfying either the conjugate boundary conditions u 0 u 1 0 or the right focal boundary conditions u 0 u 1 0 where a and f are positive valued and both lim x 0 f x x and lim x f x x exist

nonlinear eigenvalue problems for quasilinear systems the paper deals with the existence of positive solutions for the quasilinear system f u lh t f u 0 0 1 h t diag h 1 t h n t and f u f 1 u f n u assume that f i and h i are nonnegative continuous for u u 1 u n let f 0 i lim u 0f i u f u f i lim u f i u f u i 1 n f 0 maxf 1 0 f n 0 and f maxf 1 f n we prove that the boundary value problem has a positive solution for certain finite intervals of l if one of f 0 and f is large enough and the other one is small enough our methods employ fixed point theorem in a cone

positive solutions of sub superlinear sturm liouville problems in this paper we introduce the notion of a strict lower upper solution to nonlinear sturm liouville boundary value problems based on the maximum principles we establish a result of leray schauder degree on the ordered intervals induced by the pairs of strict lower and upper solutions applying the result and the fixed point index theory in cones we obtain the global existence results of positive solutions for sub superlinear sturm liouville problems

a construction procedure of iterative methods with cubical convergence we study the kantorovich convergence for parameter based methods for solving nonlinear operator equations in banach spaces we also derive a closed form of error bounds in terms of a real parameter a e 0 1

existence of positive solutions for singular higher order differential equations abstract in this paper we consider the existence of positive solutions for the following singular higher order eigenvalue problem hep 1 n u 2 n t a t f t u t u t u 2 n 1 t 0 t 1 i u 2 i 0 i u 2 i 1 0 0 i u 2 i 1 i u 2 i 1 1 0 0 i n 1 where 0 is a parameter a t may have singularity at t 0 and or 1 furthermore f t v 1 v 2 v n may also be singular at v i 0 i 1 2 n without making any monotone type assumptions we establish various lemmas and theorems for the existence of positive solutions of the hep when is in an explicit interval in addition the associated green function for the above problem is derived

existence of nodal solutions of a nonlinear eigenvalue problem with indefinite weight function abstract we investigate the existence of nodal solutions of an indefinite weight boundary value problem u r h t f u 0 0 t 1 u 0 u 1 0 where h c 0 1 changes sign the proof of our main result is based upon bifurcation techniques

existence of one signed periodic solutions of some second order differential equations via a krasnoselskii fixed point theorem this paper is devoted to study the existence of periodic solutions of the second order equation x 00 f t x where f is a caratheodory function by combining some new properties of green s function together with krasnoselskii fixed point theorem on compression and expansion of cones as applications we get new existence results for equations with jumping nonlinearities as well as equations with a repulsive or attractive singularity in this latter case our results cover equations with weak singularities and are compared with some recent results by i rachunkova m tvrdyand i vrkoc r 2002 elsevier science usa all rights reserved

existence of positive solutions for singular boundary value problem on time scales this paper deals with a class of boundary value problem of singular differential equations on time scales the conditions we used here differ from those in the majority of papers as we know an existence theorem of positive solutions is established by using the krasnosel skii fixed point theorem and an example is given to illustrate it

on the existence of positive solutions of fourth order difference equations in this paper by means of krasnosel skii s fixed point theorem the existence of positive solutions of fourth order difference equations is considered

positive solutions for one dimensional p laplacian boundary value problems with dependence on the first order derivative abstract this paper presents sufficient conditions for the existence and multiplicity of positive solutions to the one dimensional p laplacian differential equation p u a t f u u 0 subject to some boundary conditions we show that it has at least one or two or three positive solutions under some assumptions by applying the fixed point theorem

existence of positive solutions of bvps for third order discrete nonlinear difference systems in this paper we consider the following boundary value problem of discrete email protected 3u 1 k f 1 k u 1 k u 2 k 0 email protected 0 t d 3u 2 k f 2 k u 1 k u 2 k 0 email protected 0 t with the dirichlet boundary conditionu 1 0 u 1 1 u 1 t 3 0 u 2 0 u 2 1 u 2 t 3 some new results of the existence nonexistence and multiplicity are obtained by using krasnosel skii s fixed point theorem in a cone in particular it is proved that the above boundary value problem has n positive solutions under suitable conditions where n is an arbitrary positive integer

abstract existence theorems of positive solutions for nonlinear boundary value problems let rn be a bounded domain h l2 l d l h h be a unbounded linear operator and f r r be a continuous function this paper deals with the existence of positive solutions of the operator equation lu f x u u d l which is the abstract form of differential equations boundary value problems the essential conditions on l and f guaranteeing the existence of positive solution are characterized the discussion is based on the krasnoselskii s fixed point theorem of cone mapping and the fixed point index theory in cones the abstract results are applied to some differential equations boundary value problems and some known results are extended and improved

existence results for time scale boundary value problem in this paper we establish some existence results for positive solutions to a class of singular boundary value problem on time scale by using the krasnosel skii fixed point theorem two examples are presented as applications the conditions we used in this paper are different from those in d r anderson eigenvalue intervals for a two point boundary value problem on a measure chain j comput appl math 141 2002 57 64 c j chyan j henderson eigenvalues problems for nonlinear differential equations on a measure chain j math anal appl 245 2000 547 559 l h erbe a peterson positive solutions for nonlinear differential equation on a measure chain math comput modelling 32 2000 571 585 l h erbe h y wang on the existence of positive solutions of ordinary differential equations proc amer math soc 120 1994 743 748 j henderson h y wang positive solutions for nonlinear eigenvalue problems j math anal appl 208 1997 252 259 c h hong c c yeh positive solutions for eigenvalue problems on a measure chain nonlinear anal 51 2002 499 507 w c lian w f wong c c yeh on the existence of positive solutions of nonlinear differential equations proc amer math soc 124 1996 1117 1126 j liang t j xiao z c hao positive solutions of singular differential equations on measure chain comput math appl 49 2005 651 663

positive solutions of boundary value problems for third order functional difference equations the existence of positive solutions are established for the third order functional difference equation 3u n a n f n u w n 0 0 n t satisfying u n n n1 n 1 and u n n t 3 n n2 with 0 1 t 3 0 the results in this paper generalize and substantially improve recent work by agarwal and henderson on boundary value problems related to third order difference equations

existence of positive solutions for quasi linear differential equations suffic ient conditions for the existence of at least one positive solution for the following quasilinear differential equation op x i c t f x 0 are given where op u ulv 2u p 2 is a constant c e c r r f x 0 for x o f x 0 for x 0 the method used in this paper is the shooting method 2004 elsevier ltd all rights reserved

positive solutions of nonlinear functional difference equations abstract in this paper we apply a cone theoretic fixed point theorem and obtain sufficient conditions for the existence of positive solutions to some boundary value problems for a class of functional difference equations we consider analogues of sublinear or superlinear growth in the nonlinear terms

a note on bifurcation from an interval we study the global bifurcation of nonlinear sturm liouville problems of the form pu qu lambda a x f u b 0 u 0 c 0 u 0 0 b 1 u 1 c 1 u 1 0 which are not linearizable in any neighborhood of the origin c 2005 published by elsevier ltd

positive solutions of bvps for third order nonlinear difference systems abstract in this paper we consider the following discrete system boundary value problems 3 u 1 k f 1 k u 1 k u 2 k 0 k o t 3 u 2 k f 2 k u 1 k u 2 k 0 k o t with the dirichlet boundary condition u 1 0 u 1 1 u 1 t 3 0 u 2 0 u 2 1 u 2 t 3 some sufficient conditions are obtained for the existence of one or two positive solutions to the above system by using a nonlinear alternative of leray schauder type and krasnosel skii s fixed point theorem in a cone

green functions and positive solutions for boundary value problems of third order difference equations in this paper we investigate the boundary value problems for the third order nonlinear difference equation d 3u t 2 a t f u t 0 t 2 t 2 satisfying five kinds of different boundary value conditions the green functions are constructed carefully and their bounds are evaluated some verifiable criteria for the existence of at least one positive solution and two positive solutions are obtained by using the green functions and the evaluations of bounds some examples are given to demonstrate the applications of the theorems obtained

twin monotone positive solutions to a singular nonlinear third order differential equation abstract this paper discusses the existence of at least one or two nondecreasing positive solutions for the following singular nonlinear third order differential equation x t t f t x t 0 a t b x a x a x b 0 where 0 is a parameter c a b r f c a b 0 r t may be singular at t a b and f t s may be singular at s 0 green s function and the fixed point theorem of cone expansion and compression type are utilized to illustrate the results four nontrivial examples are included

positive solutions for a floquet functional boundary value problem in this paper we prove the existence of multiple positive solutions for a boundary value problem concerning a first order functional differential equation the results are obtained by using two fixed point theorems on appropriate cones in banach spaces these theorems are based on the fixed point index theory

multiple positive solutions for m point boundary value problems 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 q t f t u 0 t 0 1 subject to the boundary conditions u 0 i 1 m 2 a i u i u 1 i 1 m 2 b i u i where p s s p 2 s by using a fixed point theorem in a cone we present sufficient conditions for the existence of multiple positive solutions for the above boundary value problem

existence and iteration of positive solutions for a multipoint one dimensional p laplacian boundary value problem abstract in this paper we study the existence and iteration of positive solutions for the one dimensional p laplacian differential equation p u t q t f t u t u t 0 t 0 1 subject to the following multipoint boundary condition u 0 i 1 n 2 i u i u 1 i 1 n 2 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

on the number of positive solutions of a nonlinear algebraic system abstract in this paper we study the nonlinear algebraic system of the form e x af x where 0 is a parameter x and f x denote the column vectors col x 1 x 2 x n and col f 1 x 1 f 2 x 2 f n x n respectively with fk r r k 1 2 n 1 n and n is a positive integer a aij n n is an n n matrix and all its entries are positive numbers many problems in various areas such as difference equations boundary value problems dynamical networks stochastic process numerical analysis etc can be converted to system e applying fixed point theorems we prove results on existence uniqueness multiplicity and nonexistence of positive solutions for e

three positive solutions of boundary value problems for p laplacian difference equations in this paper existence criteria for three positive solutions of p laplacian difference equation f p u t 1 a t f u t 0 t 1 t 1 u 0 u t 2 0 oru 0 u t 1 0 are established by using the five functionals fixed point theorem as an application one example is given to illustrate the main result in this paper

positive solutions of second order two delay differential systems with twin parameter abstract the paper is concerned with the existence of positive solutions for a second order two delay differential systems with twin parameter firstly we present some sufficient conditions with the twin parameter belonging to an open rectangular region eigenvalue region to ensure the existence of positive solutions for the differential systems with singularity secondly we deal with the superlinear semipositone problem of the differential systems and establish the existence of positive solutions for the systems the proofs are based on a fixed point theorem in cones

multiple positive solutions of bvps for third order discrete difference systems this paper is concerned with the following email protected 3u 1 k f 1 k u 1 k u 2 k 0 email protected 0 t d 3u 2 k f 2 k u 1 k u 2 k 0 email protected 0 t with the dirichlet boundary conditionu 1 0 u 1 1 u 1 t 3 0 u 2 0 u 2 1 u 2 t 3 by using leggett williams fixed point theorem sufficient conditions are obtained for the existence of three positive solutions to the above system

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

on the existence of positive solutions for nonlinear differential equations with periodic boundary conditions we prove the existence of positive solutions of second order nonlinear differential equations on a finite interval with periodic boundary conditions and give upper and lower bounds for these positive solutions obtained results yield positive periodic solutions of the equation on the whole real axis provided that the coefficients are periodic

positive solutions of nonresonance semipositone singular dirichlet boundary value problems abstract in the case where the nonlinearity term is allowed to change sign we study the nonresonance semipositone singular dirichlet boundary value problem bvp x p t x f t x g t x 0 t 1 x 0 x 1 0 where 0 is a parameter 0 is a constant we derive an interval of such that for any lying in this interval the semipositone bvp has at least one positive solution if f is superlinear or sublinear the results obtained improve and extend many recent results our approach is based on krasnaselskii s fixed point theorem in cones

nodal solutions for nonlinear eigenvalue problems we are concerned with determining values of for which there exist nodal solutions of the boundary value problems u ra t f u 0 0 t 1 u o u 1 0 the proof of our main result is based upon bifurcation techniques

on eigenvalue intervals and twin eigenfunctions of higher order boundary value problems abstract in this paper we shall consider the boundary value problem y n q t y y 1 y n 2 p t y y 1 y n 2 n 2 t 1 1 y i 0 0 0 i n 3 y n 2 0 y n 1 0 0 yy n 2 1 y n 1 1 0 where 0 and are constants satisfying 0 0 0 and 0 intervals of are determined to ensure the existence of a positive solution of the boundary value problem for 1 we shall also offer criteria for the existence of two positive solutions of the boundary value problem in addition upper and lower bounds for these positive solutions are obtained for special cases several examples are included to dwell upon the importance of the results obtained

existence of solutions to a class of nonlinear second order two point boundary value problems in this paper the existence and multiplicity results of solutions are obtained for the second order two point boundary value problem u t f t u t for all t 0 1 subject to u 0 u 1 0 where f is continuous the monotone operator theory and critical point theory are employed to discuss this problem respectively in argument quadratic root operator and its properties play an important role

a generalization of concavity for finite differences abstract the concept of concavity is generalized to discrete functions u satisfying the n th order difference inequality 1 n k n u m 0 m 0 1 n and the homogeneous boundary conditions u 0 u k 1 0 u n k 1 u n n 0 for some k 1 n 1 a piecewise polynomial is constructed which bounds u below the piecewise polynomial is employed to obtain a positive lower bound on u m for m k n k where the lower bound is proportional to the supremum of u an analogous bound is obtained for a related green s function

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

positive solutions for some second order four point boundary value problems abstract in this paper the second order four point boundary value problem x t h t f t x t 0 0 t 1 x 0 a x x 1 b x is studied where 0 1 0 a b 1 and h 0 1 0 f 0 1 0 0 are nonnegative continuous functions by the use of the property of the corresponding green s function fixed point index theory leray schauder degree and upper and lower solution method some existence nonexistence and multiplicity results of positive solutions are acquired

nontrivial solutions of boundary value problems of second order difference equations we employ the critical point theory to establish the existence of nontrivial solutions for some boundary value problems of second order difference equations

nodal solutions of second order boundary value problems with superlinear or sublinear nonlinearities abstract we consider boundary value problems for nonlinear second order differential equations of the form u a t f u 0 t 0 1 u 0 u 1 0 where a c 1 0 1 0 with a t 0 0 for some t 0 0 1 and f r r is continuous with f s s 0 for s 0 we establish existence and multiplicity results for nodal solutions of the problems if either f 0 0 f or f 0 f 0 where f s s approaches f 0 and f as s approaches 0 and respectively we use bifurcation techniques to prove our main results

new fixed point theorems for mixed monotone operators and local existence uniqueness of positive solutions for nonlinear boundary value problems abstract in this article we present a new fixed point theorem for a class of general mixed monotone operators which extends the existing corresponding results moreover we establish some pleasant properties of nonlinear eigenvalue problems for mixed monotone operators based on them the local existence uniqueness of positive solutions for nonlinear boundary value problems which include neumann boundary value problems three point boundary value problems and elliptic boundary value problems for lane emden fowler equations is proved the theorems for nonlinear boundary value problems obtained here are very general

existence of positive solutions of bvps for second order nonlinear difference systems this paper is concerned with the following system d 2u i k f i k u 1 k u 2 k u n k 0 k 0 t i 1 2 nwith the dirichlet boundary conditionu i 0 u i t 2 0 i 1 2 n some new results are obtained for the existence and multiplicity of positive solutions to the above system by using nonlinear alternative of leray schauder type krasnosel skii s fixed point theorem in a cone and leggett williams fixed point theorem in particular it proves that the above system has n positive solutions under suitable conditions where n is an arbitrary integer

the probability of the quantum diffusion controlled reaction of a species pair abstract the kinetics of diffusion controlled bimolecular reaction a b p products is investigated in the case when the motion of the diffusing particle is governed by the quantum markovian master equation for a density matrix in the site representation in the framework of the discrete model of random walks definitions are given of the survival and reaction probabilities for a pair of particle species a and b and of the rate constant a method for calculating these quantities is proposed formulae are obtained for the survival and reaction probabilities and the rate constant corresponding to chemical interaction between the particles only when they are at one and the same site

a generalization of the cone expansion and compression fixed point theorem and applications abstract the classical krasnosel skii fixed point theorem concerning cone compression and expansion of norm type is extended in it the norm is replaced with some convex functional as an application the existence of positive solutions for the singular second order m point boundary value problem is considered

unilateral global bifurcation phenomena and nodal solutions for p laplacian in this paper we establish a dancer type unilateral global bifurcation result for one dimensional p laplacian problem p u m t p u g t u t 0 1 u 0 u 1 0 under some natural hypotheses on the perturbation function g 0 1 r r r we show that k p is a bifurcation point of the above problem and there are two distinct unbounded continua ck and ck consisting of the bifurcation branch ck from k p 0 where k p is the k th eigenvalue of the linear problem corresponding to the above problem as the applications of the above result we study the existence of nodal solutions for the following problem p u f t u 0 t 0 1 u 0 u 1 0 moreover based on the bifurcation result of girg and takac 2008 13 we prove that there exist at least a positive solution and a negative one for the following problem div p u f x u in u 0 on

multiple positive solutions of a discrete difference system this paper is concerned with the following system d 2u 1 k f 1 k u 1 k u 2 k 0 k 0 t d 2u 2 k f 2 k u 1 k u 2 k 0 k 0 t u 1 0 u 1 t 2 0 u 2 0 u 2 t 2 by using leggett williams fixed point theorem sufficient conditions are obtained for the existence of three positive solutions to the above system

entropy evolution in self organization process h theorem and s theorem abstract the boltzmann gibbs entropy is used as a measure of the degree of order or degree of chaoticity of states of different open systems for a set of stationary states corresponding to different values of the control parameter the renormalized to a given value of the mean effective hamiltonian entropy decreases for the processes of self organization this statement was called by yu l klimontovich pis ma zh tekh fiz 9 1983 1412 the s theorem

existence nonexistence and multiplicity of periodic solutions for a kind of functional differential equation with parameter abstract in this paper we study the existence multiplicity and nonexistence of positive periodic solutions for a kind of second order delay functional differential equation with parameter u t a t u t f t u t 0 t u t 1 t u t n t by employing the krasnoselskii fixed point theorem for a cone map where 0 is a parameter some new results are obtained as an application of our results we discuss an example

positive solutions of second order boundary value problems with sign changing nonlinear terms abstract in this paper the existence results of positive solutions are obtained for second order boundary value problem u f t u t 0 1 u 0 u 1 0 where f c 0 1 r whose sign may change the proof is based on the fixed point index theory in cones

existence of multiple positive solutions for sturm liouville like four point boundary value problem with p laplacian abstract in this paper we consider the sturm liouville like four point boundary value problem with p laplacian p u t f t u t 0 t 0 1 u 0 u 0 u 1 u 0 where p s s p 2 s p 1 by means of a fixed point theorem for operators on a cone the existence of multiple at least three positive solutions to the above boundary value problem is obtained

positive solutions and nonlinear eigenvalue problems for third order difference equations first solutions that lie in a cone intersected with an annular type region are obtained for the third order difference equation 3u t a t f u t 0 2 t t 2 satisfying the boundary conditions u 0 u 1 u t 3 0 in the cases that f is either superlinear or sublinear the second part is devoted to determining values of for which there exist positive solutions of 3u t a t f u t 0 2 t t 2 satisfying the boundary conditions u 0 u 1 u t 3 0 when both limx 0 f x x and limx f x x exist as positive real numbers

the existence of symmetric positive solutions for sturm liouville like four point boundary value problem with a p laplacian operator abstract in this paper the sturm liouville like four point boundary value problem with a p laplacian operator p u t a t f t u t 0 t 0 1 u 0 u 0 u 1 u 0 is studied where p s s p 2 s p 1 by the use of fixed point index theory leray schauder degree and upper and lower solution method some existence nonexistence and multiplicity results of symmetric positive solutions are acquired

existence and multiplicity of positive solutions of a nonlinear eigenvalue problem with indefinite weight function this paper is concerned with the existence multiplicity and stability of positive solutions of an indefinite weight boundary value problemu email protected t f u 0 0

positive solutions of boundary value problems for disfocal ordinary differential equations we study the existence of positive solutions of a nonlinear eigenvalue problem for a two point boundary value problem for a family of second order disfocal ordinary differential equations we apply a cone theoretic fixed point theorem and obtain both sufficient conditions for the existence of positive solutions and sufficient conditions for the existence of multiple positive solutions

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

numerical study of transport properties in continuum percolation the authors present numerical simulations of ac conductance for a random resistor capacitor network the conductance obeys a probability density function p g varies as g alpha 0 alpha 1 they use a highly efficient propagation algorithm to calculate the effective conductance of a long strip of a lattice at low frequencies they find that for the concentration p of conducting bonds less than the percolation threshold pc the imaginary part of conductance is proportional to frequency im geff approximately omega and the real part of conductance shows an anomalous frequency dependence re geff approximately omega 2 alpha the results of simulations in such a continuum system are in agreement with the predictions of the effective medium and the maxwell garnett approximation they also calculate the non universal dc conductivity exponents in continuum percolation the results are consistent with earlier theoretical predictions and numerical calculations

positive solutions and eigenvalue regions of two delay singular systems with a twin parameter abstract the paper is concerned with a two delay singular differential system with a twin parameter applying fixed point index theory we show the relationship between the asymptotic behaviors of nonlinearities at zero and infinity and the open regions eigenvalue regions of parameters which are correlated with delays such that the system has zero one and two positive solution s

on positive solutions of boundary value problems on the half line we study the existence of positive solutions of boundary value problems on the half line for differential equations of second order the krasnoselskii fixed point theorem on cone compression and expansion is used

semilocal convergence of a continuation method with holder continuous second derivative in banach spaces in this paper the semilocal convergence of a continuation method combining the chebyshev method and the convex acceleration of newton s method used for solving nonlinear equations in banach spaces is established by using recurrence relations under the assumption that the second frechet derivative satisfies the holder continuity condition this condition is mild and works for problems in which the second frechet derivative fails to satisfy lipschitz continuity condition a new family of recurrence relations are defined based on two constants which depend on the operator the existence and uniqueness regions along with a closed form of the error bounds in terms of a real parameter a 0 1 for the solution x is given two numerical examples are worked out to demonstrate the efficacy of our approach on comparing the existence and uniqueness regions for the solution obtained by our analysis with those obtained by using majorizing sequences under holder continuity condition on f it is found that our analysis gives improved results further we have observed that for particular values of the a our analysis reduces to those for the chebyshev method a 0 and the convex acceleration of newton s method a 1 respectively with improved results

on the existence of positive solutions of p laplacian difference equations in this paper by means of fixed point theorem in a cone the existence of positive solutions of p laplacian difference equations is considered

eigenvalue and spectral intervals for a nonlinear algebraic system abstract this paper studies the nonlinear algebraic system of the form x af x where 0 a is a positive n n square matrix x x 1 x 2 x n t f x f x 1 f x 2 f x n t the nondecreasing continuous function f is defined on 0 and f u 0 for u 0 the system covers many problems that arise in applications such as difference equations boundary value problems and dynamical networks let f 0 lim u 0 cf u u and f lim u f u u we classify the system according to six pairs of possible values of f 0 and f with the assumption that both f 0 and f exist including for each case r 0 is divided into intervals for the value of intervals that corresponds to existence multiplicity and nonexistence of positive solutions of the system respectively we then obtain intervals that contain only the eigenvalues of the nonlinear operator t af also the resolvent and the spectrum of t are determined two examples are given to show the applications of the results

on renormalisation of fluctuations at the onset of a centre manifold the author considers a dissipative reactive system driven far from thermodynamic equilibrium and sustaining a locally attractive centre manifold beyond a symmetry breaking instability the author derives a functional equation for the renormalised diffusion pressure this coefficient gives autocorrelations for intrinsic fluctuations and depends on the bifurcation parameter the system is subject to the following realistic restrictions i the temporal organisation lying beyond the instability can be accounted for by the existence of a centre manifold ii the effective equilibrium energy averaged with respect to the stationary distribution about the centre manifold is independent of the bifurcation parameter

a three point boundary value problem for nonlinear fourth order differential equations abstract in this paper the authors consider the nonlinear fourth order ordinary differential equation e u t g t f u 0 with the boundary conditions b u 0 u 1 u 0 u p u 1 0 some results on the existence and nonexistence of positive solutions to problem e b are obtained results on the existence of infinitely many positive solutions are also presented examples are included to demonstrate that the results are sharp

existence of positive solutions of boundary value problem for a discrete difference system in this paper we consider the following boundary value problem of discrete system d 2u 1 k f 1 k u 1 k u 2 k 0 k 0 t d 2u 2 k f 2 k u 1 k u 2 k 0 k 0 t with the dirichlet boundary value conditionu 1 0 u 1 t 2 0 u 2 0 u 2 t 2 some sufficient conditions are obtained for the existence of one or two positive solutions to the above system by using nonlinear alternative of leray schauder type and krasnosel skii s fixed point theorem in a cone

positive solutions of singular differential equations on measure chains this paper is concerned with singular differential equations on measure chains theorems on the existence of positive solutions and eigenvalue intervals are obtained which extend some existing results

existence of three positive solutions for some second order boundary value problems in this paper a new fixed point theorem of functional type in a cone is established with using the new fixed point theorem and imposing growth conditions on the nonlinearity the existence of three positive solutions for the boundary value problemx t f t x t x t 0 0 0 is continuous finally an example is given to illustrate the importance of results obtained

global bifurcation and nodal solutions for a sturm liouville problem with a nonsmooth nonlinearity abstract in this paper we shall establish the unilateral global bifurcation which bifurcates from the trivial solutions axis or from infinity of a class of nonlinear sturm liouville problems with nondifferentiable nonlinearity respectively as applications of the above results we shall determine the interval of r in which there exist nodal solutions for the following problem u t r a t f u 0 t 0 1 u 0 u 1 0 where a t is a positive continuous function on 0 1 f c r r but is not necessarily differentiable at the origin and infinity moreover as a special case of the above problem we shall prove more details about the existence of nodal solutions for a class of half linear eigenvalue problems