a complete classification of bifurcation diagrams of a dirichlet problem with concave convex nonlinearities abstract we study the bifurcation diagrams of positive solutions of the two point boundary value problem u x f u x 0 1 u 1 u 1 0 where f u g u h u g h c 0 c2 0 and 0 is a bifurcation parameter we assume that functions g and h satisfy hypotheses h1 h3 under hypotheses h1 h3 we give a complete classification of bifurcation diagrams and we prove that on the u plane each bifurcation diagram consists of exactly one curve which is either a monotone curve or has exactly one turning point where the curve turns to the left hence the problem has at most two positive solutions for each 0 more precisely we prove the exact multiplicity of positive solutions

multiple positive solutions of conjugate boundary value problems with singularities the existence of one or several positive solutions for some nth order differential equations with conjugate boundary conditions is obtained the approach is to employ the well known results on the existence of positive solutions for hammerstein integral equations obtained recently by the author this avoids utilizing the theory of fixed point index for compact maps defined on cones directly new properties on the kernels corresponding to the boundary value problems are provided and then employed to prove new properties of nonzero positive solutions for these boundary value problems and new inequalities on functions satisfying the conjugate boundary conditions our results improve and generalize many recent results

uniqueness results for the one dimensional p laplacian this paper is concerned with positive solutions of the boundary value problem y p 2y f y 0 y b 0 y b where p 1 b is a positive parameter assume that f is continuous on 0 changes sign from nonpositive to positive and f y yp 1 is nondecreasing in the interval of f 0 the uniqueness results are proved using a time mapping analysis

exact number of solutions of stationary reaction diffusion equations we study both existence and the exact number of positive solutions of the problem p l l u p 2u f u 0in 0 1 u 0 u 1 0 where l is a positive parameter p 1 the nonlinearity f is positive in 0 1 and f 0 f 1 0 assuming that f satisfies the condition lim s 1 f s 1 s email protected 0 where email protected 0 p 1 we study its behavior near zero and we obtain existence and exactness results for positive solutions we prove the results using the shooting method we show that there always exist solutions with a flat core for l sufficiently small as an application we prove the existence of a non negative solution for a class of singular quasilinear elliptic problems in a bounded domain in r n having a flat core in a ball

positive and compacton type solutions for a quasilinear two point boundary value problem abstract in this paper we investigate a one dimensional p laplacian problem whose nonlinearity comprises both p sublinear and p superlinear terms by studying the multiplicity of solutions to an auxiliary problem we show how convenient choices of the parameters involved yield the existence of at least three classical positive solutions satisfying hopf s boundary condition in addition we provide the existence of two distinct curves of parameters along which our problem admits at least a compacton type solution

non negative solutions for a class of non positone problems in the recent past many results have been established on non negative solutions to boundary value problems of the form where 0 f 0 0 positone problems in this paper we consider the impact on the non negative solutions when f 0 f u to be convex to guarantee uniqueness of positive solutions and f u to be appropriately concave for multiple positive solutions this is in contrast to the case of positone problems where the roles of convexity and concavity were interchanged to obtain similar results we further establish the existence of non negative solutions with interior zeros which did not exist in positone problems

on s shaped bifurcation curves for multiparameter positone problems abstract we study the existence of multiple positive solutions to the two point boundary value problem u x f u x o u 0 0 u 1 u 1 where 0 0 here f is a smooth function such that f 0 on 0 r for some 0 r in particular we consider the case when f is initially convex and then concave we discuss sufficient conditions for the existence of at least three positive solutions for a certain range independent of of we apply our results to the nonlinearity f u exp cu c u c 4 which arises in combustion theory and to the nonlinearity f u u exp c 1 u 0 fixed c 4 4 which arises in chemical reactor theory

strategic information transmission this paper develops a model of strategic communication in which a better informed sender s sends a possibly noisy signal to a receiver r who then takes an action that determines the welfare of both we characterize the set of bayesian nash equilibria under standard assumptions and show that equilibrium signaling always takes a strikingly simple form in which s partitions the support of the scalar variable that represents his private information and introduces noise into his signal by reporting in effect only which element of the partition his observation actually lies in we show under further assumptions that before s observes his private information the equilibrium whose partition has the greatest number of elements is pareto superior to all other equilibria and that if agents coordinate on this equilibrium r s equilibrium expected utility rises when agents preferences become more similar since r bases his choice of action on rational expectations this establishes a sense in which equilibrium signaling is more informative when agents preferences are more similar

optimal use of communication resources we study a repeated game with asymmetric information about a dynamic state of nature in the course of the game the better informed player can communicate some or all of his information to the other our model covers costly and or bounded communication we characterize the set of equilibrium payoffs and contrast these with the communication equilibrium payoffs which by definition entail no communication costs

population models with diffusion strong allee effect and constant yield harvesting abstract we study the steady state distribution of reaction diffusion equations with strong allee effect type growth and constant yield harvesting semipositone in heterogeneous bounded habitats assuming the exterior of the habitat is completely hostile we establish existence results for positive solutions we also establish a multiplicity result for the non harvested case we obtain our results via the method of sub super solutions

uniqueness and nonuniqueness for positive radial solutions of δu f u r 0 on considere le probleme de l unicite pour les solutions positives du probleme de dirichlet non lineaire u f u x 0 dans u 0 est une boule ou un anneau de r n et f 0 est superlineaire en u et satisfaisait f 0 x 0

positive solutions of a singular nonlinear third order two point boundary value problem abstract in this paper some existence results of positive solutions for the following singular nonlinear third order two point boundary value problem x t t f t x t 0 a t b x a x b x b 0 are established where c a b 0 f c a b 0 0 t may be singular at t a b and f t x may be singular at x 0

singular extremal solutions for supercritical elliptic equations in a ball abstract we study positive singular solutions to the dirichlet problem for the semilinear elliptic equation u f u 0 in the unit ball on r n we assume that f has the form f u u p g u where p n 2 n 2 and g u is a lower order term we first show the uniqueness of the singular solution to the problem and then study the existence of the singular extremal solution in particular we show a necessary and sufficient condition for the existence of the singular extremal solution in terms of the weak eigenvalue of the linearized problem

solvability of some fourth and higher order singular boundary value problems abstract existence results for a variety of singular fourth order boundary value problems of the form yiv f t y y y are given here our nonlinear term f may be singular at t 0 t 1 y 0 and or y 0 for example some singularities of the type y a and y b are included also we discuss and treat the extension of these results to nth order boundary value problems

the number of positive solutions of a non linear problem with discontinuous non linearity for the non linear problem where f is a discontinuous function at 1 we show that the number of non trivial positive solutions for a given real number 0 is related to the graph of a continuous function g then by studying the function g it is possible in some special cases to give for any 0 the minimal or exact number of non trivial positive solutions

exact multiplicity of positive solutions for a class of semilinear problem ii we consider the positive solutions to the semilinear problem u f u 0 in b n u 0 on b n where bn is the unit ball in rn n 1 and is a positive parameter it is well known that if is a smooth function then any positive solution to the equation is radially symmetric and all solutions can be parameterized by their maximum values we develop a unified approach to obtain the exact multiplicity of the positive solutions for a wide class of nonlinear functions u and the precise shape of the global bifurcation diagrams are rigorously proved our technique combines the bifurcation analysis stability analysis and topological methods we show that the shape of the bifurcation curve depends on the shape of the graph of function u u as well as the growth rale of

on the cauchy problem for the evolution p laplacian equations with gradient term and source abstract in this paper the authors study the equation u t div d u p 2 d u u q 1 u d u l in r n with p 2 we first prove that for 1 l p 1 the solution exists at least for a short time then for p 2 l p 1 the existence and nonexistence of global in time solutions are studied in various situations

a complete classification of bifurcation diagrams of a p laplacian dirichlet problem we study the bifurcation diagrams of positive solutions of the p laplacian dirichlet problem p u x f u x 0 1 1 p y y p 2y p u is the one dimensional p laplacian and 0 is a bifurcation parameter we assume that functions g and h satisfy hypotheses h1 h3 under hypotheses h1 h3 we give a complete classification of bifurcation diagrams and we prove that on the u plane each bifurcation diagram consists of exactly one curve which is either a monotone curve or has exactly one turning point where the curve turns to the right hence the problem has at most two positive solutions for each 0 more precisely we prove the exact multiplicity of positive solutions in addition for p 2 we give interesting examples which show the evolution phenomena of bifurcation diagrams

classification of bifurcation diagrams of a p laplacian dirichlet problem with examples abstract we study bifurcation diagrams of positive solutions of the p laplacian dirichlet problem p u x f u x 0 1 x 1 u 1 u 1 0 where p y y p 2 y p u is the one dimensional p laplacian and p 1 and 0 are two bifurcation parameters assume that f u g u h u where g h c 0 c 2 0 satisfy hypotheses h1 h5 presented herein for different values p with 1 p 2 and with p 2 we give a classification of totally six different bifurcation diagrams we prove that on the u plane each possible bifurcation diagram consists of exactly one curve with exactly one turning point where the curve turns to the right hence we are able to determine the exact multiplicity of positive solutions in addition for 1 p 2 and for p 2 we give interesting examples f u k u p 1 u q u r satisfying r q p 1 and k 0 and show complete evolution of bifurcation diagrams as evolution parameter k varies from 0 to

the set of positive solutions of semilinear equations in large balls the exact number of positive solutions of u f u 0 on finite balls in n is determined the assumptions about f u are similar to those imposed by serrin and the second author in a previous study of uniqueness of the positive solution when the spatial domain is all of n see 7 8 for finite balls of sufficiently large radius it is shown here that there are exactly two positive and hence radial solutions to this end we first prove the linear nondegeneracy of the positive solution of n this is obtained by applying the technique of monotone separation of graphs 7 to the linearised equations somewhat sharper estimates are required here see part i section 2

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

fair distribution protocols or how the players replace fortune there are n 2 players p1 p2 pn each of them having a finite alphabet a1 an and there is a probability distribution p on a a1 an the players want to choose a a according to p in such a way that pk knows only the kth component ak of a this can be done with the help of an impartial person or fortune who chooses a a according to p and informs pk on ak only but what happens if no such person is available can the players find a procedure that replaces fortune it is proved here that the answer is yes when n 4 as an application it is shown that a correlated equilibrium of a noncooperative n person game n 4 coincides with a nash equilibrium of an extended game involving in addition plain conversations only

triple positive solutions of a boundary value problem for nonlinear singular second order differential equations of mixed type with p laplacian in this paper we establish the existence of triple positive solutions of a two point boundary value problem for the nonlinear singular second order differential equations of mixed type with a p laplacian operator we also demonstrate that the results obtained can be applied to study certain higher order mixed boundary value problems finally an example is given to demonstrate the use of the main results of this paper

positive solutions for a fourth order p laplacian boundary value problem abstract in this paper we study the existence multiplicity and uniqueness of positive solutions for the fourth order p laplacian boundary value problem u p 1 u f t u u 2 i 0 u 2 i 1 0 i 0 1 here p 0 and f c 0 1 r r r 0 based on a priori estimates achieved by utilizing properties of concave functions we use fixed point index theory to establish our main results

exact multiplicity for semilinear elliptic dirichlet problems involving concave and convex nonlinearities let b be the unit ball in r n n 3 let 0 p q n 2 n 2 in 1994 ambrosetti et al found that the semilinear elliptic dirichlet problem admits at least two solutions for small 0 and no solution for large in this paper we prove that there is a critical number 0 such that this problem has exactly two solutions for 0 exactly one solution for and no solution for

bifurcation and admissible solutions for the hessian equation abstract we study the following eigenvalue problem of k hessian equation s k d 2 u k f u in b u 0 on b global bifurcation result is established for this problem as applications of the bifurcation result we determine the intervals of for the existence nonexistence uniqueness and multiplicity of radially symmetric k admissible solutions for this problem

diffusive logistic equation with constant yield harvesting i steady states we consider a reaction diffusion equation which models the constant yield harvesting to a spatially heterogeneous population which satisfies a logistic growth we prove the existence uniqueness and stability of the maximal steady state solutions under certain conditions and we also classify all steady state solutions under more restricted conditions exact global bifurcation diagrams are obtained in the latter case our method is a combination of comparison arguments and bifurcation theory

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

positive solutions of nonlinear beam equations with time and space singularities we consider the existence and multiplicity of positive solutions to a nonlinear fourth order two point boundary value problem the nonlinear term may be singular with respect to both the time and space variables in mechanics the problem describes the deformation of an elastic beam fixed at the left and supported at the right by sliding clamps by introducing height functions of the nonlinear term on some bounded sets and considering integrations of these height functions several local existence theorems are obtained

on a singular nonlinear semilinear elliptic problem where k x c2 b v9 a p 0 1 and l is a real parameter such singular elliptic problems arise in the contexts of chemical heterogeneous catalysts nonnewtonian fluids and also the theory of heat conduction in electrically conducting materials see 3 5 8 9 for a detailed discussion obviously 1 1 cannot have a solution u c2 v9 if k x is not vanishing near v however under various appropriate assumptions on k x we will obtain classical solutions of 1 1 for l belonging to a certain range and we will also obtain some uniqueness criteria here a classical solution is a solution u of 1 1 which belongs to c2 v mc v9 with u 0 in v we also study the boundary behaviour of solutions of 1 1 and we will show that the solution u of 1 1 lies in a certain holder class the special case when k x is negative and l 0 has been studied by several authors the existence and uniqueness of the solution were established by crandall rabinowitz and tartar 6 del pino 7 gomes 10 and lazer and mckenna

cooperation and effective computability a common interest game is a game in which there exists a unique pair of payoffs which strictly pareto dominates all other payoffs we consider the undiscounted repeated game obtained by the infinite repetition of such a two player stage game we show that if supergame strategies are restricted to be computable within church s thesis the only pair of payoffs which survives any computable tremble with sufficiently large support is the pareto efficient pair the result is driven by the ability of the players to use the early stages of the game to communicate their intention to play cooperatively in the future

exact multiplicity of positive solutions of a semipositone problem with concave convex nonlinearity abstract we study the exact multiplicity of positive solutions and bifurcation diagrams of the dirichlet boundary value problem u x f u 0 1 x 1 u 1 u 1 0 where 0 is a bifurcation parameter f c 0 c 2 0 satisfies f 0 0 semipositone and f is concave convex on 0 and is asymptotic superlinear assuming additional suitable conditions on f on the u plane we give a classification of totally three qualitatively different bifurcation diagrams a reversed s shaped curve a broken reversed s shaped curve and a monotone decreasing curve our results improve those in j shi r shivaji exact multiplicity of solutions for classes of semipositone problems with concave convex nonlinearity discrete contin dyn syst 7 2002 559 571 we also give an application to determine completely the exact multiplicity of positive solutions and bifurcation diagrams of the problem with cubic nonlinearity u x u a u b u c 0 1 x 1 u 1 u 1 0 0 a b c

new exact multiplicity results with an application to a population model we obtain some new exact multiplicity results for the dirichlet boundary value problem on a unit ball b n in r n we consider several classes of nonlinearities f u including both positive and sign changing cases a crucial part of the proof is to establish positivity of solutions for the corresponding linearized problem as an application we obtain exact multiplicity results for the holling tanner population model

global bifurcation of steady state solutions in this paper we study the bifurcation of steady state solutions of a reaction diffusion equation in one space variable the steady state solutions satisfy the equation a f u 0 on the interval l 0 or 0 for some nonzero function c c a for the neumann problem we use entirely different techniques to prove that s is never critical for any cubic polynomial j this implies at once that the neumann problem can have at most one nonconstant solution having a given number of maxima or minima this solution is necessarily strongly nondegenerate in the sense that zero is not contained in the spectrum of the linearized operator see 2 for the dirichlet problem the situation is far more complicated and the bifurcation diagrams undergo qualitative changes depending on the positions of the roots off for example fig 1 shows the bifurcation diagram for the positive solutions for two different cubic functions of the form f u a u u b u c it is interesting to note however that in every case we study there are at most three solutions to the dirichlet problem for each

combined effects of concave and convex nonlinearities in some elliptic problems abstract this paper deals with a class of semilinear elliptic dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results

classification and evolution of bifurcation curves for a multiparameter p laplacian dirichlet problem abstract we study the classification and evolution of bifurcation curves for the multiparameter p laplacian dirichlet problem p u x u q k 1 n a k u r k 1 0 1 x 1 q 0 0 r 1 r 2 r n n 2 a k 0 for k 1 2 n u 1 u 1 0 where p 1 p y y p 2 y p u is the one dimensional p laplacian and 0 is a bifurcation parameter and q 0 is an evolution parameter we give a classification of totally five qualitatively different bifurcation curves for different q 0 more precisely we prove that on the u plane each bifurcation curve is either a monotone curve if q 0 p 1 r n p 1 or has exactly one turning point where the curve turns to the right if q p 1 r n p 1 hence the problem has at most two positive solutions for each 0 we also show evolution of five bifurcation curves as q varies from 0 to

a complete classification of bifurcation diagrams for a class of p q laplace equations abstract we study the bifurcation problem of positive solutions for the one dimensional p q laplace equation with nonlinear term u r 1 there are five types of order relations for p q r we investigate the exact shape of the bifurcation curve in each type of the order relation we prove that there are two types of bifurcation curves that are increasing two types that are decreasing and one that is not monotone and turns exactly once moreover we study the asymptotic profile of the normalized solution u x u as u 0 or u where u denotes the l norm of u

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

existence uniqueness and nondegeneracy of positive solutions of semilinear elliptic equations we study positive solutions of the dirichlet problem a u x f u x 0 x d u x o x e ad where d is an n ball we find necessary and sufficient conditions for solutions to be nondegenerate we also give some new existence and uniqueness theorems in this paper we study positive solutions of the dirichlet problem au x f u x o x f2

computational complexity and communication coordination in two player games the main contribution of this paper is the development and application of cryptographic techniques to the design of strategic communication mechanisms one of the main assumptions in cryptography is the limitation of the computational power available to agents we introduce the concept of limited computational complexity and by borrowing results from cryptography we construct a communication protocol to establish that every correlated equilibrium of a two person game with rational payoffs can be achieved by means of computationally restricted unmediated communication this result provides an example in game theory where limitations of computational abilities of players are helpful in solving implementation problems more specifically it is possible to construct mechanisms with the property that profitable deviations are too complicated to compute

branches of radial solutions for semipositone problems abstract we consider the radially symmetric solutions to the equation u x u x for x u x 0 for x where denotes the unit ball in r n n 1 centered at the origin and 0 here r r is assumed to be semipositone 0 0 there exists at most one positive solution u such that u belongs to the unbounded branch of positive solutions further when t tp k k 0 and 1

exact multiplicity of positive solutions for a class of semilinear problems we establish an exact multiplicity result of positive solutions of u f u 0inbn u 0on bn wherebnis the unit ball fsatisfiesf changes sign only once and asymptotically sublinear or linear the nonlinearities which we are concerned with here includef u u u b c u for 0 2b candf u up uqfor 1 p q precise global bifurcation diagrams are obtained

rationality computability and nash equilibrium suppose two agents play a game each using a computable algorithm to decide what to do these algorithms being common knowledge we show that it is possible to act rationally provided we limit our attention to a natural subset of solvable games and to opponents who use rational algorithms the outcome is a nash equilibrium going further we show that rationality is possible on many domains of games and opposing algorithms but each domain requires a particular solution algorithm no one algorithm is rational on all possible domains

exact multiplicity of solutions and s shaped bifurcation curves for the p laplacian perturbed gelfand problem in one space variable abstract we study exact multiplicity of positive solutions and the bifurcation curve of the p laplacian perturbed gelfand problem from combustion theory p u x exp a u a u 0 1 x 1 u 1 u 1 0 where p 1 p y y p 2 y p u is the one dimensional p laplacian 0 is the frank kamenetskii parameter u x is the dimensionless temperature and the reaction term f u exp a u a u is the temperature dependence obeying the arrhenius reaction rate law we find explicitly a a p 0 such that if the activation energy a a then the bifurcation curve is s shaped in the u plane more precisely there exist 0 such that the problem has exactly three positive solutions for exactly two positive solutions for and and a unique positive solution for 0 and

positive solutions for a system of second order quasilinear boundary value problems abstract in this paper we study the existence and multiplicity of positive solutions for the system of second order quasilinear boundary value problems u p 1 f t u v v q 1 g t u v u 0 u 1 0 v 0 v 1 0 where p q 1 and f g c 0 1 r 2 r r 0 based on a priori estimates achieved by utilizing jensen s inequality for nonnegative concave functions and homogeneous operators we use fixed point index theory to establish the main results

uniqueness of positive solutions for some nonlinear fourth order equations abstract in this paper we study the uniqueness question of positive solutions of the two point boundary value problem u 4 t f u t r 0 is fixed andf 0 0 is inc1 a uniqueness result is proved whenfsatisfies 0 0 some examples are also given

an accurate computation of the global solution curve for the gelfand problem through a two point approximation when one solves numerically the gelfand boundary value problem in two dimensions with u u x y r x 2 y 2 and l a positive parameter email protected u 0forr 1 u 0whenr r with 10 mesh points two spurious turns appear on the solution curve when one increases the number of mesh points the spurious turns persist occurring at smaller values of l it turns out that spurious turns are avoided in the other direction by using two to six mesh points we prove this in case of two mesh points this gives us the correct form of the solution curve and the accuracy can then be improved by using a linear search on u 0 combined with shooting

uniqueness of non negative solutions of semilinear equations in rn on etudie l unicite des solutions positives classiques u x du probleme u f u 0 dans r n u x 0 quand x avec n 1 et x x 1 x n

exact multiplicity results for a p laplacian problem with concave convex concave nonlinearities we study the exact number of positive solutions of a two point dirichlet boundary value problem involving the p laplacian operator we consider the case p 2 as well as the case p 1 when the nonlinearity f satisfies f 0 0 and has two distinct simple positive zeros and such that f changes sign exactly twice on 0 note that we may allow that f changes sign more than twice on 0 some interesting examples of quartic polynomials are given in particular for f u u2 u 1 u 2 we study the evolution of the bifurcation curves of the p laplacian problem as p increases from 1 to infinity and hence are able to determine the exact multiplicity of positive solutions for each p 1

the evolution of travelling waves in fractional order autocatalysis with decay i permanent form travelling waves this paper considers a model isothermal autocatalytic reaction scheme with termination when the reaction orders m n are fractional i e 0 n and k in 0 k c where kc depends upon m and n it is further established that these wavefronts are of excitable rather than fisher kolmogorov type and have only semi infinite support that is the reaction is totally dormant ahead of the wavefront these features are in contrast to the case when m n geq 1 as studied by merkin needham and scott proc roy soc london ser a 424 1989 pp 187 209 merkin and needham j engrg math 23 1989 pp 343 356 and needham and merkin phil trans roy soc london ser a 337 1991 pp 261 274 it should be noted that the corresponding reaction diffusion equations are singular in the sense that the reaction and decay terms are not lipsch

exact multiplicity and global structure of solutions for a class of semilinear elliptic equations abstract in this paper we establish an exact multiplicity result of solutions for a class of semilinear elliptic equation we also obtain a precise global bifurcation diagram of the solution set as a result an open problem presented by c h hsu and y w shih c h hsu y w shih solutions of semilinear elliptic equations with asymptotic linear nonlinearity nonlinear anal 50 2002 275 283 is completely solved our argument is mainly based on bifurcation theory and continuation method

singular nonlinear k n k conjugate boundary value problems abstract for 1 k n 1 solutions are obtained for the boundary value problem 1 n k y n f x y y i 0 0 0 i k 1 and y j 1 0 0 j n k 1 where f x y is singular at y 0 an application is made of a fixed point theorem for operators that are decreasing with respect to a cone

exact multiplicity results for boundary value problems with nonlinearities generalizing cubic using techniques of bifurcation theory we present two exact multiplicity results for boundary value problems of the type the first result concerns the case when the nonlinearity is independent of x and behaves like a cubic in u the second one deals with a class of nonlinearities with explicit x dependence

existence and uniqueness of solutions for singular fourth order boundary value problems by mixed monotone method the existence and uniqueness are established for singular fourth order boundary value problems the theorems obtained are very general and complement previous known results

nondegeneracy and uniqueness of positive solutions for robin problem of second order ordinary differential equations and its applications abstract this article studies positive solutions of robin problem for semi linear second order ordinary differential equations nondegeneracy and uniqueness results are proven for homogeneous differential equations necessary and sufficient conditions for the existence of one or two positive solutions for inhomogeneous differential equations or differential equations with concave convex nonlinearities are obtained by making use of the nondegeneracy and uniqueness results for positive solutions of homogeneous differential equations

exact multiplicity and ordering properties of positive solutions of a p laplacian dirichlet problem and their applications we study the exact multiplicity and ordering properties of positive solutions of the p laplacian dirichlet problem

finite rationality and interpersonal complexity in repeated games a measure of complexity for repeated game strategies is studied this measure facilitates the investigation of some issues regarding finite rationality and the structure of subgame perfect equilibria of repeated games with discounting specifically the complexity of a strategy in a given repeated game is defined to be the cardinality of the induced strategy set i e the number of distinct strategies induced by the original strategy in all possible subgames we observe that this cardinality is equal to the size cardinality of the state set of the smallest automaton which can implement the strategy thus in a sense complexity is measured on the basis of the amount of computing power inherent in the strategy a measure of strategic memory is also studied the following results are obtained 1 combining two notions of bounded rationality epsilon equilibrium and finite complexity we find that every subgame perfect equilibrium of the repeated game can be approximated with regard to payoffs by a subgame perfect epsilon equilibrium of finite complexity 2 for a generic class of normal form stage games at every discount robust subgame perfect drsp equilibrium there are necessary relationships among the complexities and memories of the players strategies in the two player case strategies must be equally complex and must have equal memories 3 for a second class of two pla yer stage games we show that the payoff vectors for all drsp equilibria are obtainable via equilibria in which the players strategies are equally complex and have equal memoiies

multiplicity results for singular conjugate focal and n p problems abstract a new technique is presented which enables us to discuss the existence of one or more solutions to singular conjugate focal and n p boundary value problems our nonlinearity f t y may be singular at y 0 t 0 and or t 1

a complete classification of bifurcation diagrams of classes of a multiparameter dirichlet problem with concave convex nonlinearities abstract we study the bifurcation diagrams of positive solutions of the multiparameter dirichlet problem u x f u x 0 1 x 1 u 1 u 1 0 where f u g u h u 0 and 0 are two bifurcation parameters 0 and 0 are two given real numbers assuming that functions g and h satisfy hypotheses h1 h3 and h4 a resp h1 h3 and h4 b for fixed 0 resp 0 we give a classification of totally eight qualitatively different bifurcation diagrams we prove that on the u plane resp u plane each bifurcation diagram consists of exactly one curve which is either a monotone curve or has exactly one turning point where the curve turns to the left hence the problem has at most two positive solutions for each 0 resp 0 more precisely we prove the exact multiplicity of positive solutions in addition we give interesting examples which show complete evolution of bifurcation diagrams as resp varies

extensive form correlated equilibrium definition and computational complexity this paper defines the extensive form correlated equilibrium efce for extensive games with perfect recall the efce concept extends aumann s strategic form correlated equilibrium ce before the game starts a correlation device generates a move for each information set this move is recommended to the player only when the player reaches the information set in two player perfect recall extensive games without chance moves the set of efce can be described by a polynomial number of consistency and incentive constraints assuming p is not equal to np this is not possible for the set of ce or if the game has chance moves

double positive solutions for a nonlinear four point boundary value problem with a p laplacian operator in this paper we study the existence of positive solutions for a nonlinear four point boundary value problem with a p laplacian operator by using a three functionals fixed point theorem in a cone the existence of double positive solutions for the nonlinear four point boundary value problem with ap laplacian operator is obtained this is different than previous results

positive solutions for a system of p laplacian boundary value problems this paper is concerned with the existence and multiplicity of positive solutions for the system of p laplacian boundary value problems u i p i 1 f i t u 1 u n u i 0 u i 1 0 i 1 n where n 2 p i 1 f email protected c 0 1 xr n r i 1 n r 0 based on a priori estimates achieved by utilizing the jensen integral inequalities and r n monotone matrices we use fixed point index theory to establish the existence and multiplicity of positive solutions for the above problem

stability of solutions of a 1 dimensional p laplacian problem and the shape of the bifurcation curve abstract we consider the p laplacian boundary value problem 1 p u f u on 1 1 2 u 1 0 where p 1 p 2 p z z p 1 sgn z z r 0 f r r is c 2 and f 0 on r under these conditions the set of solutions u of 1 2 consists of the trivial solution u 0 0 together with a single connected c 2 curve s r c 0 1 1 1 r 0 under additional conditions on f the shape of s can be determined solutions of 1 2 are equilibrium solutions of a related time dependent parabolic problem and in this time dependent setting the stability of these equilibria is of interest it will be shown that the stability of solutions on s is determined by the shape of s this will first be discussed in a general setting and the results will then be applied to the specific case where s is s shaped finally similar results will be obtained for generic without any additional conditions on f

bifurcation diagrams of a p laplacian dirichlet problem with allee effect and an application to a diffusive logistic equation with predation abstract we study bifurcation diagrams of positive solutions for the p laplacian dirichlet problem p u x f u 0 1 x 1 u 1 u 1 0 f u u p 1 g u where p 1 p y y p 2 y p u is the one dimensional p laplacian 0 is a bifurcation parameter and g is of allee effect type assuming one suitable condition on g we prove that on the u plane the bifurcation diagram consists of exactly one continuous curve with exactly one turning point where the curve turns to the right hence the problem has at most two positive solutions for each 0 more precisely we are able to prove the exact multiplicity of positive solutions we give an application to a p laplacian diffusive logistic equation with predation of holling type ii functional response to this logistic equation with multiparameters more precisely we give a complete description of the structure of the bifurcation diagrams

multiple positive solutions of the one dimensional p laplacian in this work we investigate the existence of positive solutions of the p laplacian using the quadrature method we prove the existence of multiple solutions of the one dimensional p laplacian for 0 and determine their exact number for 0 2005 elsevier inc all rights reserved

existence theory for single and multiple solutions to singular positone boundary value problems abstract in this paper we present some old and new existence results for singular boundary value problems our nonlinearity may be singular in its dependent variable

a complete classification of bifurcation diagrams of classes of multiparameter p laplacian boundary value problems we study the bifurcation diagrams of positive solutions of the multiparameter p laplacian problem p u x f u x 0 1 x 1 u 1 u 1 0 where p 1 p y y p 2y p u is the one dimensional p laplacian f u g u h u and 0 and 0 are two bifurcation parameters 0 and 0 are two given real numbers assuming that functions g and h satisfy hypotheses h1 h3 and h4a resp h1 h3 and h4b for fixed 0 resp 0 we give a classification of totally eight qualitatively different bifurcation diagrams we prove that on the u plane resp u plane each bifurcation diagram consists of exactly one curve which is either a monotone curve or has exactly one turning point where the curve turns to the right hence the problem has at most two positive solutions for each 0 resp 0 more precisely we prove the exact multiplicity of positive solutions in addition for all p 1 we give interesting examples which show complete evolution of bifurcation diagrams as resp varies

a complete classification of bifurcation diagrams of a p laplacian dirichlet problem abstract we study the bifurcation diagrams of classical positive solutions u with u 0 of the p laplacian dirichlet problem p u x f q u x 0 1 x 1 u 1 0 u 1 where p 1 p y y p 2 y p u is the one dimensional p laplacian 0 is a bifurcation parameter and f q u 1 u q is defined on 0 with q 0 more precisely for different p q we give a complete classification of bifurcation diagrams of classical positive solutions on the u plane hence we are able to determine the exact multiplicity of classical positive solutions for each p q

nonlinear superlinear singular and nonsingular second order boundary value problems abstract many new existence theorems are presented for singular and nonsingular second order boundary value problems singularities at y 0 t 0 and t 1 will be discussed

three positive solutions for dirichlet problems involving critical sobolev exponent and sign changing weight abstract in this paper we study the decomposition of the nehari manifold via the combination of concave and convex nonlinearities furthermore we use this result and the lusternik schnirelman category to prove that a semilinear elliptic equation involving a sign changing weight function has at least three positive solutions

four positive solutions for a semilinear elliptic equation involving concave and convex nonlinearities abstract in this paper we study the combined effect of concave and convex nonlinearities on the number of positive solutions for a semilinear elliptic equation with the help of the nehari manifold and the center mass function we prove that there are at least four positive solutions for a semilinear elliptic equation in a finite strip with a hole