nontrivial solutions of m point boundary value problems for singular second order differential equations with a sign changing nonlinear term this paper concerns the existence of nontrivial solutions for the following singular m point boundary value problem with a sign changing nonlinear term lu t h t f t u 0 0 is a sign changing continuous function and may be unbounded from below by applying the topological degree of a completely continuous field and the first eigenvalue and its corresponding eigenfunction of a special linear operator some new results on the existence of nontrivial solutions for the above singular m point boundary value problem are obtained an example is then given to demonstrate the application of the main results the work improves and generalizes the main results of g han y wu nontrivial solutions of singular two point boundary value problems with sign changing nonlinear terms j math anal appl 325 2007 1327 1338 j sun g zhang nontrivial solutions of singular superlinear sturm liouville problem j math anal appl 313 2006 518 536

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 for nonhomogeneous boundary value problems in banach spaces abstract by using darbo fixed point theorem the existence and nonexistence of fixed point are obtained for the following integral operator t y t 0 1 g t s f s y s ds tv using these results we investigate the existence and nonexistence of positive solutions for second order nonhomogeneous local and nonlocal boundary value problems in banach spaces

positive solutions to a second order three point boundary value problem abstract the existence nonexistence and multiplicity of nonnegative solutions are established for the three point boundary value problem u t p t f u t 0 u 0 0 u 1 u where 0 1 0 1 and is a nonnegative parameter under appropriate hypotheses the key idea is that the problem of finding a nonnegative solution is transformed into the problem of finding a fixed point of a completely continuous operator the arguments involve the schauder fixed point the method of upper and lower solutions for three point boundary value problems and the leray schauder degree theory

global behavior of positive solutions of nonlinear three point boundary value problems we investigate the structure of the positive solution set for nonlinear three point boundary value problems of the form u h t f u 0 u 0 0 u 1 lambdau eta where eta epsilon 0 1 is given lambda epsilon 0 1 n is a parameter f epsilon c 0 infinity 0 infinity satisfies f s 0 for s 0 and h epsilon c 0 1 0 infinity is not identically zero on any subinterval of 0 1 our main results demonstrate the existence of continua of positive solutions of the above problem c 2004 elsevier ltd all rights reserved

existence of positive solutions for n 2 order p laplacian bvp under some suitable assumptions we show that the n 2 order non linear boundary value problems bvp 1 e 1 f p u n t f t u t u 1 t u n 1 t bc 1 u i 0 0 i 0 1 2 n 3 u n 1 1 0u n 2 0 email protected n 1 h u n 1 0 email protected 1u n 1 x u n 1 email protected 1u n x and bvp 2 e 2 f p u n t f t u t u 1 t u n 1 t bc 2 u i 0 0 i 0 1 2 n 3 u n 1 0 0u n 2 1 email protected n 1 h u n 1 0 email protected 1u n 1 x u n 1 email protected 1u n x have at least two positive solutions in c n 0 1

cr invariants of weight five in the bergman kernel abstract fefferman s program 1979 c fefferman adv math 31 131 262 of getting a biholomorphically invariant asymptotic expansion of the bergman kernel for smoothly bounded strictly pseudoconvex domains is realized in dimension 2 with the identification of universal constants according to the program the expansion is in terms of an approximately invariant smooth defining function of the domain which we refer to as fefferman s defining function and the coefficients are functions in the domain constructed by using derivatives of fefferman s defining function consequently the invariant expansion is necessarily a finite sum with a remainder term and the ambiguity estimate is crucial in the problem we get an expansion such that the boundary values of the coefficients are cr invariants of weight 5 this refines earlier results of c r graham 1987 in lecture notes in math vol 1276 pp 108 135 springer verlag new york berlin and the authors 1993 k hirachi g komatsu and n nakazawa in lecture notes in pure and appl math vol 143 pp 77 96 dekker new york the refinement becomes possible by appropriate extensions inside the domain of the cr invariants of weight 4 due to the ambiguity estimate of these extensions our expansion is optimal as far as fefferman s defining function is used a similar result for the szego kernel is also obtained

integral kahler invariants and the bergman kernel asymptotics for line bundles abstract on a compact kahler manifold one can define global invariants by integrating local invariants of the metric assume that a global invariant thus obtained depends only on the kahler class then we show that the integrand can be decomposed into a chern polynomial the integrand of a chern number and divergences of one forms which do not contribute to the integral we apply this decomposition formula to describe the asymptotic expansion of the bergman kernel for positive line bundles and to show that the cr q curvature on a sasakian manifold is a divergence

multiple positive solutions for nonlinear singular m point boundary value problem abstract in this paper we study the existence of multiple positive solutions for the following nonlinear m point boundary value problem bvp u a t f u t 0 0 t 1 u 0 i 1 m 2 a i u i u 1 i 1 k b i u i i k 1 s b i u i i s 1 m 2 b i u i where r r is an increasing homeomorphism and homomorphism and 0 0 1 k s m 2 a i b i 0 with 0 i 1 k b i i k 1 s b i 1 0 i 1 m 2 a i 1 0 1 2 m 2 1 a t c 0 1 0 f c 0 0 some new results are obtained for the existence of at least twin or triple positive solutions of the above problem by applying avery henderson and a new fixed point theorems respectively as an application some examples are included to illustrate the main results in particular our results extend and improve some known results

toeplitz operators and weighted bergman kernels abstract for a smoothly bounded strictly pseudoconvex domain we describe the boundary singularity of weighted bergman kernels with respect to weights behaving like a power possibly fractional of a defining function and more generally of the reproducing kernels of sobolev spaces of holomorphic functions of any real order this generalizes the classical result of fefferman for the unweighted bergman kernel finally we also exhibit a holomorphic continuation of the kernels with respect to the sobolev parameter to the entire complex plane our main tool are the generalized toeplitz operators of boutet de monvel and guillemin

existence of at least three solutions of a second order three point boundary value problem abstract we study existence of at least three solutions in the presence of two lower and two upper solutions of some second order nonlinear three point boundary value problem of the type x f t x x t i 0 1 x 0 0 x 1 x 0 1 0 1 the growth of f with respect to x is allowed to be quadratic we use some degree theory arguments to get the multiplicity result

nodal solutions for second order m point boundary value problems with nonlinearities across several eigenvalues abstract we study the existence of nodal solutions of the m point boundary value problem u f u 0 0 t 1 u 0 0 u 1 i 1 m 2 i u i where i q i 1 2 m 2 with 0 1 2 m 2 1 and i r i 1 2 m 2 with i 0 and 0 i 1 m 2 i 1 we give conditions on the ratio f s s at infinity and zero that guarantee the existence of nodal solutions the proofs of our main results are based upon bifurcation techniques

necessary and sufficient conditions for the existence of positive solutions of fourth order multi point boundary value problems abstract this paper investigates the existence of positive solutions of singular multi point boundary value problems of fourth order ordinary differential equation with p laplacian a necessary and sufficient condition for the existence of c 2 0 1 positive solution as well as pseudo c 3 0 1 positive solution is given by means of the fixed point theorems on cones

positive solutions of the three point boundary value problem for second order differential equations with an advanced argument abstract in this paper by using the fixed point index method we establish the existence of at least one or at least two positive solutions to the three point boundary value problem for a second order differential equation with an advanced argument u t a t f u h t 0 t 0 1 u 0 0 u u 1 where 0 1 0 and 1 0 as an application we also give an example to demonstrate our result

solvability of the φ laplacian with nonlocal boundary conditions rather mild sufficient conditions are provided for the existence of positive solutions of a boundary value problem of the form f x t c t fx t 0 email protected 0 1 x 0 l 0 x x 1 l 1 x 0 which unify several cases discussed in the literature in order to formulate these conditions one needs to know only properties of the homeomorphism f r r and have information about the level of growth of the response operator f no metric information concerning the linear operators l 0 l 1 in the boundary conditions is used except that they are positive and continuous and such that l j 1 email protected 0 1

on sign changing solution for some three point boundary value problems abstract in this paper an existence result of sign changing solution for some three point boundary value problems is obtained by using the fixed point index method

existence of sign changing solutions for some asymptotically linear three point boundary value problems abstract in this paper by using the topological degree theory and the fixed point index theory the existence of three kinds of solutions i e sign changing solutions positive solutions and negative solutions for asymptotically linear three point boundary value problems is obtained

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

on the lower order terms of the asymptotic expansion of tian yau zelditch we compute the first three coefficients of the asymptotic expansion of tian yau zelditch we also prove that in general the fcth coefficient is a polynomial of the curvature and its derivative of weight k

multiplicity results for positive solutions of some semi positone three point boundary value problems in this paper some multiplicity results for positive solutions of some singular semi positone three point boundary value problem be obtained by using the fixed point index method

nonzero solutions of hammerstein integral equations with discontinuous kernels using the theory of fixed point index we establish new results for the existence of nonzero solutions of integral equations of the form u t gk t s f s u s ds where g is a compact set in rn and k changes sign so positive solutions may not exist f satisfies caratheodory conditions and k may be discontinuous we apply our results to prove the existence of nontrivial solutions of some nonlocal boundary value problems

low dissipation carnot like heat engines at maximum efficient power we study the optimal performance of carnot like heat engines working in the low dissipation regime using the product of the efficiency and the power output also known as the efficient power as our objective function efficient power function represents a trade off between power and efficiency of a heat engine we find lower and upper bounds on the efficiency in the case of extreme asymmetric dissipation when the ratio of dissipation coefficients at the cold and the hot contacts approaches respectively zero or infinity in addition we obtain the form of efficiency for the case of symmetric dissipation we also discuss the universal features of efficiency at maximum efficient power and derive the bounds on the efficiency using a global linear irreversible framework introduced recently by one of the authors

positive solutions to a multi point boundary value problem with delay abstract the paper is concerned with the existence of positive solutions for the nonlinear multi point boundary value problems of a class of second order delay differential equations our results improve some recent results obtained in d q jiang multiple positive solutions for boundary value problems of second order delay differential equations appl math lett 15 2002 575 583 dingyong bai yuantong xu existence of positive solutions for boundary value problems of second order delay differential equations appl math lett 18 2005 621 630

positive solutions to a system of second order nonlocal boundary value problems abstract in this paper we study the existence of positive solutions to a system of second order nonlocal boundary value problems by using fixed point index theory in a cone our hypotheses imposed on nonlinearities are those which characterize systems of nonlocal boundary value problems and our boundary value conditions are expressed in terms of possibly nonlinear functions of riemann stieltjes integrals thus generalizing and unifying the boundary value conditions in the literature therefore our results cannot be routinely deduced from the ones for single nonlocal problem in the literature

fixed point theorem of leggett williams type and its application we establish a norm type cone expansion and compression fixed point theorem for completely continuous operators our theorem is then applied to prove the existence of positive solution of second order three point boundary value problem

existence of solutions of boundary value problems for second order functional differential equations abstract in this paper we deal with the boundary value problem x f t x x t x x t x 0 x 0 c 1 c 2 c 1 c 2 r x j 0 x 1 x j 0 where f car j r c r r c r c r j 0 1 1 a j a 0 1 a j and a 0 1 are two special sets of functionals and x j is the restriction of x to j we find sufficient conditions for the existence of solutions of the above problem the proof is based on the leray schauder degree theory

on existence and multiplicity of positive solutions to singular multi point boundary value problems the existence and multiplicity of positive solutions are established for the multi point boundary value problem p t u t f t u t 0 0 t 1 u 0 j 1maju xj w 1 j 1mbjw xj where w t p t u t aj bj 0 with 0 j 1maj 1 and j 1mbj 1 xj 0 1 with 0 x1 x2 xm 1 under certain conditions on p and f the arguments are based upon the positivity of the green s function and the krasnosel skii fixed point theorem

three solutions for three point boundary value problems abstract in this paper we study the existence of at least three solutions for the three point nonlinear boundary value problems u t a t f u 0 0 t 1 u 0 0 u 1 u where 0 1 0 1 a c 0 1 0 and f c r r without any monotonicity assumptions on the nonlinear term f by using the increasing operator theory and approximation process we prove that the three point boundary value problems has at least three solutions

positive solutions for singular systems of three point boundary value problems this paper investigates the following singular systems of nonlinear second order three point boundary value problems u f t v email protected 0 1 v g t u email protected 0 1 u 0 v 0 0 u 1 email protected h v 1 email protected h where email protected 0 1 0 email protected 1 f and g may be singular at t 0 and or t 1 under some weaker conditions the existence of positive solutions is obtained by applying the fixed point theorem of cone expansion and compression two examples are then presented to demonstrate the application of our main results

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

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

on the existence of positive solution for second order multi points boundary value problems here we are concerned with the existence of positive solution for autonomous and nonautonomous second order systems with multi points boundary conditions for nonautonomous systems we use the schauder s fixed point theorem in a suitable banach space while for autonomous ones using fixed point theorems is usually useless because of the existence of trivial solution and for this we employed a method based on the implicit function theorem and topological degree in order to verify the obtained results we have considered some definite systems to verify the results numerically

positive solutions of singular three point boundary value problems for the one dimensional p laplacian abstract we use the fixed point index theory to establish the existence of at least one or two positive solutions for the singular three point boundary value problems f p y a t f y t 0 0

global structure of positive solutions for nonlocal boundary value problems involving integral conditions abstract in this paper we consider the nonlinear eigenvalue problems u h t f u 0 0 t 1 u 0 0 u 1 0 1 u s d a s where 0 1 u s d a s is a stieltjes integral with a nondecreasing and a t is not a constant on 0 1 h c 0 1 0 and h t 0 on any subinterval of 0 1 f c 0 0 and f s 0 for s 0 and f 0 f 0 f 0 lim s 0 f s s f lim s f s s we investigate the global structure of positive solutions by using global bifurcation techniques

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

three positive solutions of a nonlinear three point boundary value problem abstract in this paper existence criteria for three positive solutions of the nonlinear three point boundary value problem u t a t u t b t u t h t f u 0 t 0 1 u 0 0 u 1 u are established by using the leggett williams fixed point theorem an example is also included to illustrate the importance of the result obtained

construction of boundary invariants and the logarithmic singularity of the bergman kernel in which case the coefficients aj are expressed by the weyl invariant theory in terms of the riemannian curvature tensor and its covariant derivatives the bergman kernel s counterpart of the time variable t is a defining function r of the domain by f1 and bs the formal singularity of k at a boundary point p is uniquely determined by the taylor expansion of r at p thus one has hope of expressing modulo on 1 r and modulo o r in terms of local biholomorphic invariants of the boundary provided r is appropriately chosen in f3 fefferman proposed to find such expressions by reducing the problem to an algebraic one in invariant theory associated with cr geometry and indeed expressed modulo on 19 r invariantly by solving the reduced problem partially the solution in f3 was then completed in beg to give a full invariant expression of modulo on 1 r but the reduction is still

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

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

a class of concave operators with applications abstract in this paper we provide some properties of a class of concave operators and apply these results in discussing three point boundary value problems for differential equations and nonlinear volterra integral equations

positive solutions for nonlinear three point boundary value problems on time scales abstract let t be a time scale such that 0 t t consider the following three point boundary value problem on time scales u t a t f t u t 0 t 0 t u 0 u 0 0 u u t where 0 0 0 t 0 t and d t 1 0 by using fixed point theorems in cones some new and general results are obtained for the existence of single and multiple positive solutions of the above problem in particular our criteria generalize and improve some known results

heat engines at optimal power low dissipation versus endoreversible model the low dissipation model and the endoreversible model of heat engines are two of the most commonly studied models of machines in finite time thermodynamics in this paper we compare the performance characteristics of these two models under optimal power output we point out a basic equivalence between them in the linear response regime

nodal solutions for m point boundary value problems using bifurcation methods abstract in this paper we first obtain some results on the structure of solution sets of some m point boundary value problems then using these results we obtain some multiplicity results for nodal solutions of m point boundary value problems the method to show our main results is based on the structure of solution sets due to p h rabinowitz

optimization induced by stability and the role of limited control near a steady state a relationship between stability and self optimization is found for weakly dissipative heat devices the effect of limited control on operation variables around an steady state is such that after instabilities the paths toward relaxation are given by trajectories stemming from restitution forces which improve the system thermodynamic performance power output efficiency and entropy generation statistics over random trajectories for many cycles shows this behavior as well two types of dynamics are analyzed one where an stability basin appears and another one where the system is globally stable under both dynamics there is an induced trend in the control variables space due to stability in the energetic space this behavior translates into a preference for better thermodynamic states and thus stability could favor self optimization under limited control this is analyzed from the multiobjective optimization perspective as a result the statistical behavior of the system is strongly influenced by the pareto front the set of points with the best compromise between several objective functions and the stability basin additionally endoreversible and irreversible behaviors appear as very relevant limits the first one is an upper bound in energetic performance connected with the pareto front and the second one represents an attractor for the stochastic trajectories

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

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

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

a sharper condition for the solvability of a three point second order boundary value problem letf 0 1 r2 rbe a function satisfying caratheodory s conditions ande t l1 0 1 let 0 1 r 1 1 be given this paper is concerned with the problem of existence of a solution for the three point boundary value problem formula omitted this problem was studied earlier by gupta ntouyas and tsamatos when 1 and when 1 with 1 in the general case this problem was studied by gupta as a multi point boundary value problem in this paper sharper existence conditions are obtained for the solvability of the above boundary value problem in the general case

existence of nontrivial solutions for a nonlinear sturm liouville problem with integral boundary conditions abstract this paper deals with the existence of nontrivial solutions for a nonlinear singular sturm liouville problem with integral boundary conditions

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

existence and multiplicity results for some three point boundary value problems abstract using the method of upper and lower solutions and some degree theory arguments we establish the existence of at least three solutions of some second order nonlinear differential equations of the type x f t x x t i 0 1 subject to nonlinear three point boundary conditions x 0 0 x 1 g x 0 1 the growth of f with respect to x is allowed to be quadratic

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

positive solutions of three point boundary value problems for systems of nonlinear second order ordinary differential equations abstract in this paper we study the three point boundary value problems for systems of nonlinear second order ordinary differential equations of the form u f t v t 0 1 v g t u t 0 1 u 0 v 0 0 u u 1 v v 1 under some conditions we show the existence and multiplicity of positive solutions of the above problem by applying the fixed point index theory in cones

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

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

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

positive solutions of second order three point boundary value problems with change of sign we study the existence of positive solutions of the second order three point boundary value problems t a t f y t 0 0 t 1 y 0 0 y 1 y n where 0 1 0 1 we show the existence of at least one positive solution by applying the krasnoselskii fixed point theorem in a cone here a t is allowed to changes sign on 0 1 applications of our results are provided to yield positive radial solutions of some elliptic boundary value problems on an annulus

positive solutions to a singular third order three point boundary value problem with an indefinitely signed green s function abstract we determine a green s function for the singular three point third order bvp u t a t f t u t 0 t 1 u 0 u 1 u 0 and then we apply the classical krasnosel ski s fixed point theorem on an also new cone the emphasis is mainly that although this bvp does not admit a positive green s function the solution obtained is still positive in our approach we find out that 17 24 1 our technique is a combination of the above fixed point theorem and properties of the corresponding vector field

multiplicity of sign changing solutions for some four point boundary value problem abstract in this paper we obtain using leray schauder degree theory some multiplicity results for sign changing solutions of a four point boundary value problem we assume the existence of a pair of strict lower and upper solutions and some additional conditions on the nonlinear term f

optimization of stochastic thermodynamic machines the study of stochastic thermodynamic machines is one of the main topics in nonequilibrium thermodynamics in this study within the framework of fokker planck equation and using the method of characteristics of partial differential equation as well as the variational method performance of stochastic thermodynamic machines is optimized according to the external potential with the irreversible work w irr or the total entropy production vardelta s mathrm tot equivalently reaching its lower bound properties of the optimal thermodynamic machines are discussed with explicit expressions of upper bounds of work output w power p and energy efficiency eta are presented to illustrate the results obtained typical examples with optimal protocols external potentials are also presented

a fundamentally simple approach to a singular boundary value problem abstract existence results by means of a simple approach for the 3rd order differential equation x t t f t x t x t x t 0 t 1 satisfying the three point boundary value conditions x 0 x x 1 0 are given where 0 1 is a fixed point in contrast to the usual case 1 2 1 f t x y z 0 for any t 0 1 x 0 y z r and the map t is positive on 0 1 and suitable singular at the end points furthermore the obtained solution x t is positive and concave on 0 1 in addition without any monotonicity assumption on the nonlinearity we prove the existence of a sequence of such solutions with lim n x n 0 our principal tools are very simple applications on the plane of the well known from combinatorial topology sperner s lemma in comparison with other classical approaches like fixed point or degree theorems

positive solutions of fourth order nonlinear singular boundary value problems abstract we consider the existence of positive solutions for the following fourth order singular sturm liouville boundary value problem 1 p t p t u t g t f t u 0 0 t 1 1 u 0 1 u 0 0 1 u 1 1 u 1 0 2 u 0 2 lim t 0 p t u t 0 2 u 1 2 lim t 1 p t u t 0 where g p may be singular at t 0 and or 1 moreover f t x may also have singularity at x 0 the existence and multiplicity theorems of positive solutions for the fourth order singular sturm liouville boundary value problem are obtained by using the first eigenvalue of the corresponding linear problems our results significantly extend and improve many known results including singular and nonsingular cases

multiple positive solutions of four point nonlinear boundary value problems for a higher order p laplacian operator with all derivatives abstract in this paper we study the existence of multiple positive solutions for nonlinear four point boundary value problems for a higher order p laplacian operator with all derivatives some new results are obtained for the multiplicity of positive solutions by applying the avery henderson fixed point theorem and the leggett williams fixed point theorem in a cone which is different from the previous approaches

positive solution of three point boundary value problem for the one dimensional p laplacian with singularities abstract in the paper we deal with positive solutions of the following nonlinear three point singular boundary value problem with a p laplacian operator p u q t f t u 0 0 t 1 subject to u 0 g u 0 0 u 1 u 0 or u 0 u 0 u 1 g u 1 0 where f t u may be singular at u 0 and q t may be singular at t 0 1 new existence principles are established

entropy generation and unified optimization of carnot like and low dissipation refrigerators the connection between carnot like and low dissipation refrigerators is proposed by means of their entropy generation and the optimization of two unified compromise based figures of merit their optimization shows that only a limited set of heat transfer laws in the carnot like model are compatible with the results stemming from the low dissipation approximation even though there is an agreement of the related physical spaces of variables a comparison between two operation regimes and relations among entropy generation efficiency cooling power and power input are obtained with emphasis on the role of dissipation symmetries the results extend previous findings for heat engines at maximum power conditions

positive solutions of nonlinear three point boundary value problems abstract let a c 0 1 b c 0 1 0 let 1 t be the unique solution of the linear boundary value problem u t a t u t b t u t 0 t 0 1 u 0 0 u 1 1 we study the existence of positive solutions to the nonlinear boundary value problem u t a t u t b t u t h t f u 0 t 0 1 u 0 0 u u 1 where 0 0 and f c 0 0 we show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones

positive solutions for singular second order three point boundary value problems abstract in this paper the singular three point boundary value problem u t h t f t u 0 0 t 1 u 0 0 u 1 u where 0 1 0 1 is considered under some conditions concerning the first eigenvalue corresponding to the relevant linear operator h t is allowed to be singular at t 0 1 and f may be singular at u 0 the existence of a positive solution is obtained by a fixed index point

existence and multiplicity of symmetric positive solutions for three point boundary value problem in this paper we are concerned with the existence and multiplicity of symmetric positive solutions for the following second order three point boundary value problem u t a t f t u t 0 0 t 1 u t u 1 t u 0 u 1 u 1 2 where a 0 1 0 is symmetric on 0 1 and maybe singular at t 0 and t 1 f 0 1 0 0 is continuous and f u is symmetric on 0 1 for all u 0 growth conditions are imposed on f which yield the existence of at least one or at least two positive solutions our proof based on krasnoselskii s fixed point theorem in a cone