positive radial solutions and non radial bifurcation for semilinear elliptic equations in annular domains abstract we discuss the existence and multiplicity of positive radial solutions and the non radial bifurcation of u f u 0 in and u 0 on where is an annular domain of r n n 2 we prove that if f u 0 for u 0 and lim u f u u then there exists 0 such that there are at least two positive radial solutions for each 0 at least one for and none for if f 0 0 lim u 0 f u u 1 and uf u 1 e f u for u 0 e 0 then there exists a variational solution for 0 1 where 1 is the least eigenvalue of if f 0 0 lim u 0 f u u 0 and lim u f u u then there exists at least one positive radial solution for any 0 we obtain some precise multiplicity results for narrow annulus and show that the non radial bifurcation occurs if the growth of f u is rapid enough as u

positive periodic solutions of singular systems with a parameter abstract the existence and multiplicity of positive periodic solutions for second order non autonomous singular dynamical systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter our results provide a unified treatment for the problem and significantly improve several results in the literature the proof of our results is based on the krasnoselskii fixed point theorem in a cone

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

positive solutions of generalized nonlinear logistic equations via sub super solutions abstract let be a smooth bounded domain in r n n 1 let m n be two nonnegative functions defined in and let r n r n be a continuous and strictly monotone mapping we consider the existence and nonexistence of positive solutions for nonlinear problems involving the laplacian of the form div u m x f u n x g u in u 0 on where 0 is a real parameter and f g 0 0 are continuous functions modeled by f t t q and g t t r with 0 q r the subdiffusive equidiffusive and superdiffusive cases are all treated and some qualitative properties of the solutions are also given as a byproduct we obtain results in the case of a roughly speaking sublinear nonlinearity f and n 0 we point out that some of our results are new even for the usual p laplacian our main tool is the sub supersolutions method combined with some estimates on related nonlinear problems

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

nontrivial solutions for p laplacian systems abstract the paper deals with the existence and nonexistence of nontrivial nonnegative solutions for the sublinear quasilinear system div u i p 2 u i f i u 1 u n 0 in u i 0 on i 1 n where p 1 is a bounded domain in r n n 2 with smooth boundary and f i i 1 n are continuous nonnegative functions let u u 1 u n u i 1 n u i we prove that the problem has a nontrivial nonnegative solution for small 0 if one of lim u 0 f i u u p 1 is infinity if in addition all lim u f i u u p 1 is zero we show that the problem has a nontrivial nonnegative solution for all 0 a nonexistence result is also obtained

positive radial solutions for quasilinear systems in an annulus abstract we show that either superlinearity or sublinearity assumptions can guarantee the existence of positive radial solutions for quasilinear systems involving the p laplacian

convex solutions of boundary value problems we establish two criteria for the existence of convex solutions for a boundary value problem arising from the study of the existence of convex radial solutions for the monge ampere equations we shall use fixed point theorems in a cone

a new existence theory for single and multiple positive periodic solutions to volterra integro differential equations with impulse effects this paper presents a new existence theory for single and multiple positive periodic solutions to a kind of nonautonomous volterra integro differential equations with impulse effects existence is established by using krasnoselskii fixed point theorem in cones this paper extends some previous results and reports some new results about impulsive differential equation

positive periodic solutions of functional differential equations with impulses and a parameter by applying the well known leggett williams multiple fixed point theorem this paper investigates the existence of multiple positive periodic solutions of functional differential equations with impulses and a parameter

flat surfaces in the hyperbolic 3 space in this paper we give a conformal representation of flat surfaces in the hyperbolic 3 space using the complex structure induced by its second fundamental form we also study some examples and the behaviour at infinity of complete flat ends

positive solutions for nonlinear problems involving the one dimensional ϕ laplacian abstract let a b r m l 1 and 0 be a real parameter let l be the differential operator given by l u u r x u where r r is an odd increasing homeomorphism and 0 r l 1 we study the existence of positive solutions for problems of the form l u m x f u in u 0 on where f 0 0 is a continuous function which is roughly speaking sublinear with respect to our approach combines the sub and supersolution method with some estimates on related nonlinear problems we point out that our results are new even in the cases r 0 and or m 0

positive solutions for a three point boundary value problem the second order three point boundary value problem x t 2x t h t f t x t t 0 1 x 0 0 x x 1 is considered under some conditions concerning the first eigenvalue of the relevant linear operator where 0 1 is a constant h t is allowed to be singular at t 0 and t 1 the existence of positive solutions is studied by means of fixed point index theory

multiplicity results for nonlinear periodic fourth order difference equations with parameter dependence and singularities abstract this paper is devoted to the study of nonlinear singular and non singular fourth order difference equations coupled with periodic boundary value conditions in the paper some existence and nonexistence results are given the results are deduced from krasnoselskii s fixed point theorems in cones an exhaustive study of the green s function related to a linear fourth order problem is done

positive periodic solutions of singular systems of first order ordinary differential equations the existence and multiplicity of positive periodic solutions for first non autonomous singular systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter the proof of our results is based on the krasnoselskii fixed point theorem in a cone

a new existence theory for positive periodic solutions to functional differential equations abstract this paper deals with a new existence theory for positive periodic solutions to a kind of nonautonomous functional differential equation by employing the fixed point theorem in cones applying the general theorems established to several biomathematical models the paper improves some previous results and obtains some new results

eigenvalues and the one dimensional p laplacian we consider the boundary value problem p u f t u 0 with p 1 t 0 1 u 0 u 1 0 and with 0 the value of is chosen so that the boundary value problem has a positive solution in addition we derive an explicit interval for such that for any in this interval the existence of a positive solution to the boundary value problem is guaranteed in addition the existence of two positive solutions for in an appropriate interval is also discussed

positive solutions and eigenvalue intervals of nonlocal boundary value problems with delays abstract the paper is concerned with the delay differential equation u b t f u t 0 satisfying u t 0 for t 0 and u 1 g 0 1 u t d t where 0 1 u t d t denotes the riemann stieltjes integral by applying the fixed point theorem in cones we show the relationship between the asymptotic behaviors of the quotient f u u at zero and infinity and the open intervals eigenvalue intervals of the parameter such that the problem has zero one and two positive solution s if g t t by using a property of the riemann stieltjes integral the above nonlocal boundary value problem educes a three point boundary value problem with delay for which some similar results are established

symmetric positive solutions for p laplacian fourth order differential equations with integral boundary conditions this paper investigates the existence and multiplicity of symmetric positive solutions for a class of p laplacian fourth order differential equations with integral boundary conditions the arguments are based upon a specially constructed cone and the fixed point theory for cones the nonexistence of a positive solution is also studied

existence of positive periodic solutions for a functional differential equation with a parameter abstract in this paper we study the existence multiplicity and nonexistence of positive periodic solutions for a kind of nonautonomous functional differential equation by employing the fixed point theorem in cones some new results are obtained as an application of our results we discuss the existence of a positive periodic solution for a class of models of blood cell production with a parameter which has not been investigated by using previous methods

multiple positive solutions of some boundary value problems abstract we study the existence of multiple positive solutions of the equations u t u subject to linear boundary conditions we show that there are at least two positive solutions if t u is superlinear at one end point zero or infinity and sublinear at the other applications of these results are provided to yield multiple positive solutions of some elliptic boundary value problems on an annulus

complete flat surfaces with two isolated singularities in hyperbolic 3 space abstract we construct examples of flat surfaces in h 3 which are graphs over a two punctured horosphere and classify complete embedded flat surfaces in h 3 with only one end and at most two isolated singularities

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 three point boundary value problems for p laplacian dynamic equations on time scales abstract the five functionals fixed point theorem is applied to investigate the existence of at least three positive solutions of three point boundary value problems for p laplacian dynamic equations on time scales

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

a homotopic deformation along p of a leray schauder degree result and existence for u p 2u ƒ t u 0 u 0 u t 0 p 1 soit f 0 1 r r une fonction continue et soit o p r r definie par o p s s p 2 s pour p fixe 1 on considere le probleme de dirichlet suivant o p u f t u 0 u 0 u t 0 ou t est un nombre reel positif

multiple eigenvalues for singular hammerstein integral equations with applications to boundary value problems new results on the existence of multiple positive eigenvalues for singular hammerstein integral equations are obtained the radius of the spectrum of a linear hammerstein integral operator is first employed to obtain a better upper bound for the eigenvalues we seek these results are applied to treat some second order ordinary differential equations with two point three point and some periodic boundary value problems

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

a necessary and sufficient condition of positive solutions for nonlinear singular differential systems with four point boundary conditions in this paper we concert with the existence of positive solution for the following nonlinear singular differential system with four point boundary conditions x f t y y g t x ax 0 email protected 0 email protected 1 email protected 1 0 y 0 ay x 1 y 1 by x 2 where 0 0 by structuring upper and lower solution and using schauder fixed point theorem a necessary and sufficient condition for the existence of positive solutions is established an example is worked out to illustrate our main result

triple positive solutions of boundary value problems for p laplacian dynamic equations on time scales a new triple fixed point theorem is applied to investigate the existence of at least three positive solutions of boundary value problems for p laplacian dynamic equations on time scales

a necessary and sufficient condition of existence of positive solutions for nonlinear singular differential systems in this paper by means of monotone iterative technique a necessary and sufficient condition of the existence of positive solution for a class of nonlinear singular differential system is established the results of the existence and uniqueness of the positive solution and the iterative sequence of solution are given in the end two classes extending boundary value differential systems are discussed and some further results are obtained

positive periodic solutions of functional differential equations abstract we consider the existence multiplicity and nonexistence of positive periodic solutions for the periodic equation x t a t g x x t b t f x t t where a b c r 0 are periodic 0 a t dt 0 0 b t dt 0 f g c 0 0 and f u 0 for u 0 g x is bounded t is a continuous periodic function define f 0 lim u 0 f u u f lim u f u u i0 number of zeros in the set f 0 f and i number of infinities in the set f 0 f we show that the equation has i0 or i positive periodic solution s for sufficiently large or small 0 respectively

on the number of positive solutions of systems of nonlinear dynamic equations on time scales in this paper we consider the following n dimensional second order nonlinear system on time scalesu d d t email protected t f u s t 0 email protected a b twith the sturm liouville boundary email protected a email protected d a 0 cu s b email protected d s b 0 where u u 1 u n a diag a 1 a n b diag b 1 b n c diag c 1 c n d diag d 1 d n let f email protected i 1 nlim u 0f i u email protected and f email protected i 1 email protected email protected f i u email protected define i 0 number of zeros in the set f 0 f and i number of infinities in the set f 0 f by using fixed point index theory we show that i if i 0 1 or 2 then there exist l 0 0 such that the system has i 0 positive solution s for l l 0 ii if i 1 or 2 then there exist l 0 0 such that the system has i 0 positive solution s for 0 0 respectively

existence and uniqueness of positive solution for singular boundary value problem this paper presents two sufficient conditions which guarantee the existence and uniqueness of a positive solution for a class of singular boundary value problems

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

on the existence of positive radial solutions for nonlinear elliptic equations in annular domains abstract we study the existence of positive radially symmetric solutions of u g x f u 0 in annulus with dirichlet dirichlet neumann boundary conditions we show that the equation has a positive radial solution on any annulus if f and f are positive and f is superlinear at 0 and

on the existence of positive solutions for semilinear elliptic equations in the annulus abstract we study the existence of positive radial solutions of u g x u 0 in annuli with dirichlet dirichlet neumann boundary conditions we prove that the problems have positive radial solutions on any annulus if is sublinear at 0 and

positive solutions of singular boundary value problems for nonlinear differential systems in this paper by constructing a special cone and applying the fixed index theory in the cone the existence of positive solutions for nonlinear ordinary differential systems with singularities is investigated and an example is developed to demonstrate our main results

existence and nonexistence of positive solutions for second order time scale systems abstract this paper is concerned with the following system on time scale t u i t f i u 1 t u 2 t u n t 0 t 0 t t u i 0 0 u i 2 t i 1 2 n where 0 t t and t 0 by using the theory of the fixed point index we investigate the effect of 2 t on the existence and nonexistence of positive solution for the above system in sublinear cases the results obtained are even new for the special cases of difference system and differential system as well as in the general time scale setting

existence of nontrivial solutions for discrete nonlinear two point boundary value problems in this paper by using strongly monotone operator principle and critical point theory the existence of nontrivial solutions for discrete nonlinear two point boundary value problems is established two illustrative examples are given in the last part of the paper

structure of a class of singular boundary value problem with superlinear effect abstract this paper investigates the structure of solutions of singular boundary value problem with superlinear effect it is proved that the closure of positive solution set possesses a maximal subcontinuum c i e a maximal closed connected subset of solutions which comes from 0 and tends to 0 finally as a corollary the existence of multiple positive solutions and the behavior of solutions according to parameter are obtained

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

integration with respect to closable set functions abstract integration with respect to closable set functions is used to treat perturbations to schrodinger semigroups the method is illustrated by perturbations generated by potentials with zero relative bound relative to the free hamiltonian operator of a finite non relativistic quantum system and by the attractive 1 r 2 potential for a single non relativistic particle

ribaucour transformations for flat surfaces in the hyperbolic 3 space abstract we consider ribaucour transformations for flat surfaces in the hyperbolic 3 space h 3 we show that such transformations produce complete embedded ends of horosphere type and curves of singularities which generically are cuspidal edges moreover we prove that these ends and curves of singularities do not intersect we apply ribaucour transformations to rotational flat surfaces in h 3 providing new families of explicitly given flat surfaces h 3 which are determined by several parameters for special choices of the parameters we get surfaces that are periodic in one variable and surfaces with any even number or an infinite number of embedded ends of horosphere type

positive solutions of some second order nonlinear singular differential equations abstract with new schemes the existence of the positive solutions is proved to some second order nonlinear singular boundary value problems and initial value problems which have higher order singularities

surfaces of constant curvature in r3 with isolated singularities abstract we prove that finite area isolated singularities of surfaces with constant positive curvature k 0 in r 3 are removable singularities branch points or immersed conical singularities we describe the space of immersed conical singularities of such surfaces in terms of the class of real analytic closed locally strictly convex curves in s 2 with admissible cusp singularities characterizing when the singularity is actually embedded in the global setting we describe the space of peaked spheres in r 3 i e compact convex surfaces of constant curvature k 0 with a finite number of singularities and give applications to harmonic maps and constant mean curvature surfaces

positive solutions of even order system periodic boundary value problems we study a class of even order system boundary value problems with periodic boundary conditions a series of criteria are obtained for the existence of one two any arbitrary number and even a countably infinite number of positive solutions criteria for the nonexistence of positive solutions are also derived as for the second order case our results extend improve and supplement those in the literature for scalar and system boundary value problems several examples are given to demonstrate the applications moreover we obtain conditions for system periodic boundary value problems of a different form to have nontrivial solutions by transforming our main results to such problems

existence multiplicity and dependence on a parameter for a periodic boundary value problem the authors consider the boundary value problem y 2 y g t f y 0 0 t 2 y 0 y 2 y 0 y 2

on the number of positive solutions of nonlinear systems abstract we prove that appropriate combinations of superlinearity and sublinearity of f u with respect to at zero and infinity guarantee the existence multiplicity and nonexistence of positive solutions to boundary value problems for the n dimensional system u h t f u 0 0 is defined by u u 1 u n where u u 1 u n and covers the two important cases u u and u u p 2 u p 1 our methods employ fixed point theorems in a cone

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

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 existence of multiple positive solutions for ϕ laplacian multipoint boundary value abstract in this paper we consider the following multipoint boundary value problem with one dimensional laplacian x t q t f t x t x t 0 t 0 1 x 0 i 1 n 2 i x i x 1 i 1 n 2 i x i where is an odd and increasing homeomorphism i 0 1 with 0 1 2 n 2 1 i and i are nonnegative constants and f t x t x t is continuous and allowed to change sign by fixed point theorems we obtain new results on the existence of at least three positive solutions of this boundary value problem which includes and improves some related results in the relevant literature

a necessary and sufficient condition for existence of positive solutions of nonlinear boundary value problems abstract we study the nonlinear boundary value problem u f t u u u t 0 1 u 2 i 0 u 2 i 1 0 i 0 1 and obtain a necessary and sufficient condition for the existence of symmetric positive solutions we also discuss the application of our result to the special case where f is a power function of u and its derivatives moreover similar conclusions for a more general higher order boundary value problem are established our analysis mainly relies on the lower and upper solution method

periodic solutions to non autonomous second order systems abstract we establish the existence of periodic solution of a class of non autonomous second order systems x x v t x 0 where v t x v 1 t x v n t x if lim x v i t x x 0 i 1 n uniformly in t and v is bounded below or above for appropriate ranges of

multiple positive solutions for a superlinear problem a topological approach we study the multiplicity of positive solutions for a two point boundary value problem associated to the nonlinear second order equation u f x u 0 we allow x f x s to change its sign in order to cover the case of scalar equations with indefinite weight roughly speaking our main assumptions require that f x s s is below 1 as s 0 and above 1 as s in particular we can deal with the situation in which f x s has a superlinear growth at zero and at infinity we propose a new approach based on topological degree which provides the multiplicity of solutions applications are given for u a x g u 0 where we prove the existence of 2n 1 positive solutions when a x has n positive humps and a x is sufficiently large

a note on a superlinear indefinite neumann problem with multiple positive solutions abstract we prove the existence of three positive solutions for the neumann problem associated to u a t u 1 0 assuming that a t has two positive humps and 0 t a t d t is large enough actually the result holds true for a more general class of superlinear nonlinearities

processes associated with evolution equations abstract conditions are given which guarantee the boundedness of the operator valued set function associated with a semigroup and a spectral measure the result is applied to represent the solution of a hyperbolic evolution equation in terms of a path space integral the representation which has been obtained by t ichinose applies to the dirac and wave equations in two space time dimensions a further application is given for the schrodinger equation in the momentum representation

existence of a positive solution for one dimensional singular p laplacian problems and its parameter dependence article history we consider one dimensional singular p laplacian problems of the form q 1 and may be singular at t 0a nd ort 1 using fixed point techniques combined with the partially ordered structure of banach space we establish some new and more general existence multiplicity and nonexistence results we also study the dependence of the positive solution u t on the parameter t hat is

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

a multiplicity result for generalized laplacian systems with multiparameters abstract in this paper we consider the existence nonexistence and multiplicity of a positive solution for a gelfand type generalized laplacian system with a singular indefinite weight and a vector parameter by using the upper and lower solution method and fixed point index theory we obtain a global multiplicity result with respect to the parameter

on the generalized weyl problem for flat metrics in the hyperbolic 3 space abstract the paper deals with the study of complete embedded flat surfaces in h 3 with a finite number of isolated singularities we give a detailed information about its topology conformal type and metric properties we show how to solve the generalized weyl s problem of realizing isometrically any complete flat metric with euclidean singularities in h 3 which gives the existence of complete embedded flat surfaces with a finite arbitrary number of isolated singularities

nonnegative solutions to nonlocal boundary value problems for systems of second order differential equations dependent on the first order derivatives abstract in this paper we consider nonlocal boundary value problems for systems of second order differential equations with dependence on the first order derivatives and deviating arguments by using a fixed point theorem due to avery and peterson sufficient conditions are obtained that guarantee the existence of at least three nonnegative solutions to such problems we investigate our problem both for delayed and advanced arguments i i and also for the case when i t i t t t 0 1 in all cases arguments i i can change the character on 0 1 so in some subinterval i of 0 1 they can be delayed in i and advanced in 0 1 i some remarks concern also the case when differential equations do not depend on the first order derivatives examples illustrate some results

existence and multiplicity results for nonlinear boundary value problems this paper studies the existence of positive solutions for a class of boundary value problems of elliptic degenerate equations by using bifurcation and fixed point index theories in the frame of approximation arguments the criteria of the existence multiplicity and nonexistence of positive solutions are established

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

double positive solutions of three point boundary value problems for p laplacian dynamic equations on time scales a new double fixed point theorem is applied to investigate the existence of at least double positive solutions of three point boundary value problems for p laplacian dynamic equations on a time scale

positive periodic solutions of higher dimensional nonlinear functional difference equations abstract by using a well known fixed point index theorem we study the existence multiplicity and nonexistence of positive t periodic solution s to the higher dimensional nonlinear functional difference equations of the form x n 1 a n x n h n f x n n n z where a n diag a 1 n a 2 n a m n h n diag h 1 n h 2 n h m n a j h j z r z z are t periodic j 1 2 m t 1 0 x z r m f r m r where r m x 1 x m t r m x j 0 j 1 2 m r x r x 0