csi usage over parallel fading channels under jamming attacks a game theory study consider a parallel channel with m independent flat fading subchannels there exists a smart jammer which has possession of a copy of perfect channel state information csi measured and sent back by a receiver to its transmitter under this model a class of two person zero sum games is investigated where either achievable mutual information rate or chernoff bound is taken as the underlying pay off function with the strategy space of each player determined by respective power control and hopping functions more specifically we have tackled and answered the following three fundamental questions the first one is about whether the transmitter and jammer should hop or fully use all degrees of freedom over the entire parallel channels given the full csi available to both of them i e to hop or not to hop the second question is about the impact of sending back csi on system performance considering that the smart jammer can exploit csi to further enhance its interference effects i e to feedback or not to feedback the last question is about whether the amount of feedback information can be reduced given the mutual restrictions between transmitter and jammer i e when to feedback and when not to

positive and negative solutions for a class of kirchhoff type problems on unbounded domain abstract in this paper we study the existence of multiple positive and negative solutions for a class of kirchhoff type problems on an unbounded domain using the variational methods we show that our problem admits at least two positive and two negative solutions under different conditions a cut off functional is utilized to obtain the bounded palais smale sequences

copolymer networks the spectrum of scaling dimensions abstract we explore the intersection properties of stars of random and self avoiding walks we show how the corresponding scaling exponents govern the scaling behavior of copolymer networks in solution we derive and calculate these exponents from a renormalization group analysis of a corresponding edwards hamiltonian our third order spectrum of exponents calculated by field theoretic renormalization shows remarkable features all exponents are scaling dimensions of composite power of field operators convexity of the spectrum allows for a multifractal interpretation and the 2d limit has no simple kac formula like structure

mutual information games in multiuser channels with correlated jamming we investigate the behavior of two users and one jammer in an additive white gaussian noise awgn channel with and without fading when they participate in a noncooperative zero sum game with the channel s input output mutual information as the objective function we assume that the jammer can eavesdrop on the channel and can use the information obtained to perform correlated jamming we also differentiate between the availability of perfect and noisy information about the user signals at the jammer under various assumptions on the channel characteristics and the extent of information available at the users and the jammer we show the existence or otherwise nonexistence of a simultaneously optimal set of strategies for the users and the jammer and characterize those strategies whenever they exist

universality class of trails in two dimensions a trail is a walk on a lattice that may visit a site more than once but a bond at most once we have carried out transfer matrix studies of trails on the square lattice and of hybrid walks that interpolate between self avoiding walks and trails the results are in agreement with the same universal exponents as self avoiding walks however the finite size corrections are much larger than for self avoiding walks an explanation in terms of an irrelevant variable with scaling index is given

nontrivial solutions of kirchhoff type problems via the yang index abstract we obtain nontrivial solutions of a class of nonlocal quasilinear elliptic boundary value problems using the yang index and critical groups

topological bifurcation of relative equilibria for the kirchhoff 8 vortex problem abstract in this article we prove necessary and sufficient conditions for the existence of local and global bifurcations of relative equilibria of the 8 vortex problem applying the equivariant bifurcation theory we prove that from the families of regular concentric squares forming relative equilibria bifurcate relative equilibria whose shape is more complicated

the existence of constrained minimizers for a class of nonlinear kirchhoff schrodinger equations with doubly critical exponents in dimension four abstract in this paper the existence and nonexistence of energy minimizer of the kirchhoff schrodinger energy function with prescribed l 2 norm in dimension four are considered the energy infimum values are completely classified in terms of coefficient and exponent of the nonlinearity the sharp existence results of global constraint minimizers for both the subcritical and critical exponent cases are obtained and the criticality is in the sense of both sobolev embedding and gagliardo nirenberg inequality our results also show the delicate difference between the case without a trapping potential function and the one with potential function

the multiplicity of positive solutions for a class of nonlocal elliptic problem abstract in this paper using the theory of fixed point index we prove some results on the multiplicity of positive solutions for a class of nonlocal elliptic problem

existence and multiplicity of solutions for a nonlocal problem with critical sobolev exponent abstract in this work we are interested in considering the following nonlocal problem a b u 2 d x u u 2 2 u u q 2 u x u 0 x where r n n 4 is a smooth bounded domain a 0 b 0 1 q 2 0 and 2 2 n n 2 is the critical sobolev exponent by using the variational method and the critical point theorem some existence and multiplicity results are obtained

correlation functions of dense polymers and c 2 conformal field theory antisymmetric correlation functions of the model of dense lattice polymers are proved to be given by the generalized kirchhoff theorem in the continuum limit they coincide with the correlation functions of the free complex grassmann field that corresponds to the non unitary conformal field theory cft with c 2 explicit expressions for the correlation functions are found these do not obey standard wick rules due to the presence of zero mode nevertheless the complex grassmann field can be considered as primary with conformal weight it is shown that the natural space of states wherein the operators of the theory act is the krein space with indefinite metric

positive solutions for kirchhoff type equations with critical exponent in rn abstract in this paper we study the following nonlinear kirchhoff type equation 0 1 a b r n u 2 d x u u 2 2 u h x x r n u d 1 2 r n where a 0 b 0 n 3 2 2 n n 2 0 and h l 2 2 1 r n 0 is nonnegative by using the variational method we obtain the existence of positive solutions for eq 0 1 under some assumptions on a b

existence and multiplicity of solutions for a quasilinear nonlocal problem abstract in this paper we establish two critical points theorems for functional which is not defined on the whole space but c 1 on a closed subset as applications we study the existence and multiplicity of solutions for a class of kirchhoff type equations with bounded nonlocal term

stationary kirchhoff problems involving a fractional elliptic operator and a critical nonlinearity this paper deals with the existence and the asymptotic behavior of non negative solutions for a class of stationary kirchhoff problems driven by a fractional integro differential operator lk and involving a critical nonlinearity in particular we consider the problem m u 2 lku f x u u 2s 2uin u 0in rn where rn is a bounded domain 2s is the critical exponent of the fractional sobolev space hs rn the function f is a subcritical term and is a positive parameter the main feature as well as the main difficulty of the analysis is the fact that the kirchhoff function m could be zero at zero that is the problem is degenerate the adopted techniques are variational and the main theorems extend in several directions previous results recently appeared in the literature

new exact exponents for two dimensional self avoiding walks the author establishes using standard coulomb gas methods the values of a new set of geometrical exponents that have been previously conjectured these exponents give for any p the number of configurations of p two dimensional self avoiding walks of the same length l which are attached by their ends

conformal invariance and universality in finite size scaling the universal relation between critical exponents and the amplitude of the correlation length divergence as a function of finite size at the critical point of two dimensional systems is shown to be a consequence of conformal invariance both periodic and free boundary conditions are considered

correlated jamming on mimo gaussian fading channels we consider a zero sum mutual information game on multiple input multiple output mimo gaussian rayleigh fading channels the players are an encoder decoder pair as the maximizer and a jammer as the minimizer of the mutual information between the input and the output of the channel there are total power constraints on both the jammer and the encoder also the jammer has access to the encoder output we find the unique saddle point of this game and prove the somewhat surprising result that the knowledge of the channel input is useless to the jammer

existence and multiplicity of positive solutions for a class of kirchhoff laplacian type problems this paper deals with the existence and multiplicity of positive solutions for a class of kirchhoff laplacian type problems in whole r3 the multiplicity of solutions is established by variational methods and ljusternik schnirelmann theory

two dimensional o n model in a staggered field nienhuis truncated o n model gives rise to a model of self avoiding loops on the hexagonal lattice each loop having a fugacity of n we study such loops subjected to a particular kind of staggered field w which for n has the geometrical effect of breaking the three phase coexistence linked to the three colourability of the lattice faces we show that at t 0 for w 1 the model flows to the ferromagnetic potts model with q n2 states with an associated fragmentation of the target space of the coulomb gas for t 0 there is a competition between t and w which gives rise to multicritical versions of the dense and dilute loop universality classes via an exact mapping and numerical results we establish that the latter two critical branches coincide with those found earlier in the o n model on the triangular lattice using transfer matrix studies we have found the renormalization group flows in the full phase diagram in the t w plane with fixed n superposing three copies of such hexagonal lattice loop models with staggered fields produces a variety of one or three species fully packed loop models on the triangular lattice with certain geometrical constraints possessing integer central charges 0 c 6 in particular we show that benjamini and schramm s rgb loops have fractal dimension df 3 2

on the existence and multiplicity of solutions for a class of singular elliptic problems abstract in this paper we prove the existence and multiplicity of solutions for a class of elliptic problems with singular coefficients we also prove the existence of a sign changing solution for a brezis nirenberg type problem with hardy potential and singular coefficients our proofs are based on the krasnoselskii genus the concentration compactness principle of lions and the linking theorem

analysis of an on off jamming situation as a dynamic game the process of communication jamming can be modeled as a two person zero sum noncooperative dynamic game played between a communicator a transmitter receiver pair and a jammer we consider a one way time slotted packet radio communication link in the presence of a jammer where the data rate is fixed and 1 in each slot the communicator and jammer choose their respective power levels in a random fashion from a zero and a positive value 2 both players are subject to temporal energy constraints which account for protection of the communicating and jamming transmitters from overheating the payoff function is the time average of the mean payoff per slot the game is solved for certain ranges of the players transmitter parameters structures of steady state solutions to the game are also investigated the general behavior of the players strategies and payoff increment is found to depend on a parameter related to the payoff matrix which me call the payoff parameter and the transmitters parameters when the payoff parameter is lower than a threshold the optimal steady state strategies are mixed and the payoff increment constant over time whereas when it is greater than the threshold the strategies are pure and the payoff increment exhibits oscillatory behavior

positive solutions for a quasilinear elliptic equation of kirchhoff type this paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the type m w u 2dx du f x u email protected u 0 email protected email protected where w is a smooth bounded domain of n m is a positive function and f has subcritical growth

concentration phenomena for a class of fractional kirchhoff equations in rn with general nonlinearities abstract in this paper we study the following class of fractional kirchhoff problems e 2 s m e 2 s n u s 2 s u v x u f u in r n u h s r n u 0 in r n where e 0 is a small parameter s 0 1 n 2 s is the fractional laplacian v r n r is a positive continuous function m 0 r is a kirchhoff function satisfying suitable conditions and f r r fulfills berestycki lions type assumptions of subcritical or critical type using suitable variational arguments we prove the existence of a family of positive solutions u e which concentrates at a local minimum of v as e 0

multiple positive solutions for kirchhoff type of problems with singularity and critical exponents abstract in this paper we study multiplicity of positive solutions for a class of kirchhoff type of equations with the nonlinearity containing both singularity and critical exponents we obtain two positive solutions via the variational and perturbation methods

signed and sign changing solutions for a kirchhoff type equation in bounded domains abstract the main concern of this article is a kirchhoff type equation of the form m u 2 u f u where is a bounded smooth domain in r n with n 3 and is a positive parameter under certain assumptions on m and f the existence results of signed and sign changing solutions are established for large and when converges to infinity the asymptotic behavior of these solutions is also studied the proofs are based on a careful study of the ground state and least energy nodal solutions of an auxiliary problem which is constructed by making a refined truncation on m furthermore we get the ground state and least energy nodal solutions and prove the energy doubling property for all 0 under more restricted assumptions on m and f

infinitely many radial solutions for kirchhoff type problems in rn abstract in this paper we concern with a class of kirchhoff type problems in r n by using the fountain theorem we obtain three existence results of infinitely many radial solutions for the problem

on kirchhoff type equations with critical sobolev exponent abstract we study the following brezis nirenberg problem of kirchhoff type a b u 2 d x u u q 2 u u 2 u in u 0 on where r 4 is a bounded domain with the smooth boundary 2 q 4 and a b are positive parameters we obtain some new existence and nonexistence results depending on the values of the above parameters which improve some known results

critical exponents of manhattan hamiltonian walks in two dimensions from potts and o n models we consider a set of hamiltonian circuits filling a manhattan lattice i e a square lattice with alternating traffic regulation we show that the generating function with fugacityz of this set is identical to the critical partition function of aq state potts model on an unoriented square lattice withq1 2 z the set of critical exponents governing correlations of hamiltonian circuits is derived using a coulomb gas technique these exponents are also found to be those of an o n vector model in the low temperature phase withn q1 2 z the critical exponents in the limitz 0 are then those of spanning trees q 0 and of dense polymers n 0 t tc corresponding to a conformal theory with central chargec 2 this shows that the manhattan orientation and the hamiltonian constraint of filling all the lattice are irrelevant for the infrared critical properties of hamiltonian walks

global bifurcation and positive solution for a class of fully nonlinear problems in this paper we study global bifurcation phenomena for the following kirchhoff type problem m u x 2 d x u f x u in u 0 on where m is a continuous function under some natural hypotheses we show that 1 a m 0 0 is a bifurcation point and there is a global continuum c emanating from 1 a m 0 0 where 1 a denotes the first eigenvalue of the above problem with f x s a x s as an application of the above result we study the existence of positive solution for this problem with asymptotically linear nonlinearity

infinitely many positive solutions for kirchhoff type problems abstract this paper is concerned with the existence of infinitely many positive solutions to a class of kirchhoff type problem a b u 2 d x u f x u in and u 0 on where is a smooth bounded domain of r n a b 0 0 and f r r is a caratheodory function satisfying some further conditions we obtain a sequence of a e positive weak solutions to the above problem tending to zero in l with f being more general than that of k perera z zhang nontrivial solutions of kirchhoff type problems via the yang index j differential equations 221 2006 246 255 z zhang k perera sign changing solutions of kirchhoff type problems via invariant sets of descent flow j math anal appl 317 2006 456 463

ground state solutions to kirchhoff type transmission problems with critical perturbation abstract a class of kirchhoff type transmission problems with critical perturbation is studied unlike other studies on elliptical equations with critical growth a ground state solution is obtained using a perturbation method instead of verifying that the mountain pass level is lower than the critical energy which is used to verify the ps condition

the nehari manifold for a kirchhoff type problem involving sign changing weight functions abstract this paper examines a class of kirchhoff type equations that involve sign changing weight functions using nehari manifold and fibering map the existence of multiple positive solutions is established

existence of nontrivial solutions for kirchhoff type variational inclusion system in r n abstract in this paper we consider the following kirchhoff type variational inclusion system a b r n u 2 dx u v x u 1 f u v in r n c d r n v 2 dx v v x v 2 f u v in r n with u v h 1 r n where n 2 and f r 2 r is a locally lipschitz function and i f u v i 1 2 are the partial generalized gradients in the sense of clarke under proper growth conditions on the nonlinearity f the existence of nontrivial solutions for the above system is established our approach is variational based on the theories of nonsmooth analysis

exact multileg correlation functions for the dense phase of branching polymers in two dimensions we consider branching polymers on the planar square lattice with open boundary conditions and exactly calculate correlation functions of k polymer chains that connect two lattice sites with a large distance r apart for odd number of polymer chains k we find that besides the standard power law factor the leading term also has a logarithmic multiplier

remarks on an elliptic equation of kirchhoff type abstract we present a short survey on the nonlocal elliptic boundary value problem m u 2 d x u f x u in u 0 on where is a smooth bounded domain of r n m is a positive function and f has subcritical growth

boundary critical behavior of d 2 self avoiding walks on correlated and uncorrelated vacancies in this paper we present exact results for the critical exponents of interacting self avoiding walks with ends at a linear boundary effective interactions are mediated by vacancies correlated and uncorrelated on the dual lattice by choosing different boundary conditions several ordinary and special regimes can be described in terms of clusters geometry and of critical and lowtemperature properties of the mathcal o n 1 model in particular the problem of boundary exponents at the point is fully solved and implications for point universality are discussed the surface crossover exponent at the special transition of noninteracting self avoiding walks is also interpreted in terms of percolation dimensions

a uniqueness result for a nonlocal equation of kirchhoff type and some related open problem abstract we study the uniqueness of solution for the following boundary value problem involving a nonlocal equation of kirchhoff type a b u 2 d x u f u in u 0 here is a bounded open set in r n with smooth boundary a b are positive real numbers and f r r is a continuous function in particular we give an answer to an open problem recently proposed by b ricceri

on a p kirchhoff equation via fountain theorem and dual fountain theorem abstract in this paper we show the existence of infinite solutions to the kirchhoff type quasilinear elliptic equation m u p x u p d x p 1 p u x u p 2 u f x u in a smooth bounded domain r n with nonlinear boundary condition u p 2 u u p 2 on the method we used here is based on fountain theorem and dual fountain theorem

exact results for fully directed polymer networks in two dimensions the authors study a connected polymer network in two dimensions with a specified topology consisting of identical long and fully directed chains the exact values of the bulk critical exponent gamma g and the surface critical exponent gamma g are obtained rigorously

existence and concentration result for the kirchhoff type equations with general nonlinearities in this paper we study the existence and concentration behaviors of positive solutions to the kirchhoff type equations varepsilon 2 m left varepsilon 2 n int mathbf r n nabla u 2 mathrm d x right delta u v x u f u quad rm in mathbf r n quad u in h 1 mathbf r n n geqq 1 where m and v are continuous functions under suitable conditions on m and general conditions on f we construct a family of positive solutions u varepsilon varepsilon in 0 tilde varepsilon which concentrates at a local minimum of v after extracting a subsequence ek

polynomial fusion rings of w extended logarithmic minimal models the countably infinite number of virasoro representations of the logarithmic minimal model lm p p can be reorganized into a finite number of w representations with respect to the extended virasoro algebra symmetry w using a lattice implementation of fusion we recently determined the fusion algebra of these representations and found that it closes albeit without an identity for p 1 here we provide a fusion matrix realization of this fusion algebra and identify a fusion ring isomorphic to it we also consider various extensions of it and quotients thereof and introduce and analyze commutative diagrams with morphisms between the involved fusion algebras and the corresponding quotient polynomial fusion rings one particular extension is reminiscent of the fundamental fusion algebra of lm p p and offers a natural way of introducing the missing identity for p 1 working out explicit fusion matrices is facilitated by a further enlargement based on a pair of mutual moore penrose inverses intertwining bet

the existence of nontrivial solutions for the critical kirchhoff type problem in rn abstract in this paper we study the problem 0 1 a b r n u 2 d x u v x u f u g x u 2 1 in r n where n 3 a b 0 when n 3 and 0 is small under suitable conditions on v f and g we prove 0 1 has two nontrivial solutions when n 4 and g x 1 we also obtain the existence and non existence results

existence and concentration of ground state solutions for a class of kirchhoff type problems abstract this paper is concerned with the following singularly perturbed kirchhoff type problem e 2 a e b r 3 u 2 d x u v x u f u x r 3 u h 1 r 3 where e 0 is a small parameter a b 0 are two constants v c r 3 r and f c r r is of super linear growth at infinity and satisfies neither the usual ambrosetti rabinowitz type condition nor monotonicity condition on f u u 3 by using some new techniques and subtle analyses we prove that there exists a constant e 0 0 determined by v and f such that for e 0 e 0 the above problem has a ground state solution concentrating around global minimum of v in the semi classical limit our results are available to the case that f u u s 2 u for s 2 6 and extend the existing results concerning the case that f u u s 2 u for s 4 6

traveling salesman problem conformal invariance and dense polymers we propose that the statistics of the optimal tour in the planar random euclidean traveling salesman problem is conformally invariant on large scales this is exhibited in the power law behavior of the probabilities for the tour to zigzag repeatedly between two regions and in subleading corrections to the length of the tour the universality class should be the same as for dense polymers and minimal spanning trees the conjectures for the length of the tour on a cylinder are tested numerically

w extended fusion algebra of critical percolation two dimensional critical percolation is the member lm 2 3 of the infinite series of yang baxter integrable logarithmic minimal models lm p p we consider the continuum scaling limit of this lattice model as a rational logarithmic conformal field theory with extended w w2 3 symmetry and use a lattice approach on a strip to study the fundamental fusion rules in this extended picture we find that the representation content of the ensuing closed fusion algebra contains 26 w indecomposable representations with eight rank1 representations 14 rank 2 representations and four rank 3 representations weidentifytheserepresentationswithsuitablelimitsofyang baxterintegrable boundary conditions on the lattice and obtain their associated w extended characters the latter decompose as finite non negative sums of w irreducible characters of which 13 are required implementation of fusion on the lattice allows us to read off the fusion rules governing the fusion algebra of the 26 representations and to construct an explicit cayley table the closure of these representations among themselves under fusion is remarkable confirmation of the proposed extended symmetry

a lattice model of uniform star polymers the authors present monte carlo and exact enumeration results for three and four arm stars on a variety of lattices they estimate the exponents for the number of stars and the mean square end to end length of a branch and compare these results with scaling and renormalisation group predictions

on ground state solutions for a kirchhoff type equation with critical growth in this paper with the aid of variational method and concentration compactness principle a positive ground state solution is obtained for a class of kirchhoff type equations with critical growth a b r 3 u 2 d x u u 5 k x u q 1 x r 3 u d 1 2 r 3 where 0 is a parameter 2 q 6 and k satisfies some conditions

existence of a positive solution for a kirchhoff problem type with critical growth via truncation argument abstract in this paper we shall show an existence result of a positive solution for a kirchhoff problem type in a bounded domain of r n that is for the problem m u 2 d x u f x u u 2 2 u in u 0 on we shall study the asymptotic behavior of this solution when converges to infinity our approach is based on the variational method an appropriated truncated argument and a priori estimates to obtain the solution

multiplicity of positive solutions for a class of critical sobolev exponent problems involving kirchhoff type nonlocal term abstract we study a class of critical sobolev exponent problems involving kirchhoff type nonlocal term a b u 2 d x u u 5 g x u u q 1 x u 0 x where r 3 is a bounded domain a b 0 1 q 2 and g c r satisfies some conditions by the variational method we obtain two positive solutions moreover we prove that there exists a positive ground state solution by the nehari method

infinitely many positive solutions for a p x kirchhoff type equation this paper is concerned with the existence of infinitely many positive solutions to a class of p x kirchhoff type problem by means of a direct variational approach and the theory of the variable exponent sobolev spaces we establish the existence of infinitely many distinct positive solutions whose w1 p x norms and l norms tend to zero under suitable hypotheses about nonlinearity

existence results of positive solutions of kirchhoff type problems abstract in the present paper we use variational methods to prove two existence results of positive solutions of the following kirchhoff type problems a b u 2 u f x u in u 0 on one deals with the asymptotic behaviors of f near zero and infinity and the other deals with 4 superlinear of f at infinity

berestycki lions conditions on ground state solutions for kirchhoff type problems with variable potentials based on the strategy introduced by chen and tang adv nonlinear anal 9 496 515 2020 and some new tricks we prove that the nonlinear problem of kirchhoff type a b r3 u 2dx u v x u f u x r3 in h1 r3 admits two classes of ground state solutions under the general berestycki lions assumptions on the nonlinearity f which are almost necessary conditions as well as some weak assumptions on the potential v moreover we also give a simple minimax characterization of the ground state energy our results improve and extend recent theorems in several directions

on a critical kirchhoff type problem abstract in the present paper we study a kirchhoff type problem involving the critical sobolev exponent we give sufficient conditions for the sequentially weakly lower semicontinuity and the palais smale property of the energy functional associated to the problem

the sign changing solutions for nonlinear elliptic problem with carrier type abstract in this paper using the fixed point index method we are concerned with the existence of sign changing solutions of the following problem 0 1 a b u x d x u f u x in u x 0 x on where a 0 b 0 and r n is a bounded open set with smooth boundary and 1

a note on a nonlinear elliptic problem with a nonlocal coefficient abstract in this paper we investigate a nonlocal and nonlinear elliptic problem p a u 2 d x u u u p in u 0 on where n 3 r n is a bounded domain with smooth boundary a is a nondegenerate continuous function p 1 and r we show several effects of the nonlocal coefficient a on the structure of the solution set of p we first introduce a scaling observation and describe the solution set by using that of an associated semilinear problem this allows us to get unbounded continua of solutions u of p a rich variety of new bifurcation and multiplicity results are observed we also prove that the nonlocal coefficient can induce up to uncountably many solutions in a convenient way lastly we give some remarks from the variational point of view

the critical neumann problem of kirchhoff type in this paper we study the critical neumann problem of kirchhoff type by using the variational method and the concentration compactness argument the existence and multiplicity of nontrivial solutions are obtained

two positive solutions for the kirchhoff type elliptic problem with critical nonlinearity in high dimension abstract we investigate the kirchhoff type elliptic problem with critical nonlinearity 1 u 2 d x u u q u 2 1 u 0 in u 0 on where n 5 r n is a bounded domain with smooth boundary 0 r 2 2 n n 2 and q 1 2 1 we prove the existence of two solutions of it via the variational method since n 5 and 0 the uniqueness assertion for the associated limiting problem may fail this causes serious difficulties in controlling concentrating palais smale sequences we overcome these by introducing new techniques for a mountain pass type solution we utilize the limit function of the fibering maps of the concentrating palais smale sequence this tool is based on our careful setting of nehari type sets on the other hand a suitable modification to a concentrating minimizing sequence enables us to obtain a global minimum solution this is the first work which proves the multiplicity of positive solutions of the kirchhoff type critical problem in high dimension

positive solution for a superlinear kirchhoff type problem with a parameter abstract this paper is devoted to a nonlinear kirchhoff type problem depending on a real function and a nonnegative parameter on a smooth bounded domain of r n n 2 we show that if the nonlinearity is subcritical and superlinear at zero and infinity then there exists a positive value such that the kirchhoff type problem has at least one positive solution for any value of the parameter less than the positive value the main tools are variational methods critical point theory and iterative techniques

sign changing solutions of kirchhoff type problems via invariant sets of descent flow we obtain sign changing solutions of a class of nonlocal quasilinear elliptic boundary value problems using variational methods and invariant sets of descent flow

sign changing and multiple solutions of kirchhoff type problems without the p s condition abstract the existence of nontrivial solutions of kirchhoff type equations is an important nonlocal quasilinear problem in this paper we use minimax methods and invariant sets of descent flow to prove two interesting existence theorems for the following 4 superlinear kirchhoff type problems without the p s condition one concerning the existence of a nontrivial solution and the other one concerning the existence of sign changing solutions and multiple solutions a b u 2 u f x u in u 0 on

multiple and nodal solutions for parametric neumann problems with nonhomogeneous differential operator and critical growth abstract we consider a parametric neumann problem with nonhomogeneous differential operator and critical growth combining variational methods based on critical point theory with suitable truncation techniques and flow invariance arguments we show that for all large the problem has at least three nontrivial smooth solutions two of constant sign one positive the other negative and the third nodal we also study the asymptotic behavior of all solutions obtained when converges to infinity the interesting point is that we do not impose any restrictions to the behavior of the nonlinear term f at infinity our work unifies and sharply improves several recent papers

existence and multiplicity of solutions for kirchhoff type equations abstract in this paper the existence and multiplicity of weak solutions are obtained for a class of kirchhoff type problems with dirichlet boundary value conditions by using the mountain pass theorem the local linking theorem the fountain theorem and the symmetric mountain pass lemma in critical point theory

shannon meets von neumann a minimax theorem for channel coding in the presence of a jammer we study the setting of channel coding over a family of channels whose state is controlled by an adversarial jammer by viewing it as a zero sum game between a finite blocklength encoder decoder team and the jammer the encoder decoder team choose stochastic encoding and decoding strategies to minimize the average probability of error in transmission while the jammer chooses a distribution on the state space to maximize this probability the min max value of the game is equivalent to channel coding for a compound channel we call this the shannon solution of the problem the max min value corresponds to finding a mixed channel with the largest value of the minimum achievable probability of error when the min max and max min values are equal the problem is said to admit a saddle point or von neumann solution while a shannon solution always exists the communicating team s problem is nonconvex for finite blocklengths whereby a von neumann solution may not exist despite this we show that the min max and max min values become equal asymptotically in the large blocklength limit for all but finitely many rates we explicitly characterize this limiting value as a function of the rate and obtain tight finite blocklength bounds on the min max and max min value as a corollary we get an explicit expression for the epsilon capacity of a compound channel under stochastic codes the first such result to the best of our knowledge our results demonstrate a deeper relation between the compound channel and mixed channel than was previously known they also show that the conventional information theoretic viewpoint articulated via the shannon solution coincides asymptotically with the game theoretic one articulated via the von neumann solution key to our results is the derivation of new finite blocklength upper bounds on the min max value of the game via a novel achievability scheme and lower bounds on the max min value obtained via the linear programming relaxation based approach we introduced in 2

the pivot algorithm a highly efficient monte carlo method for the self avoiding walk the pivot algorithm is a dynamic monte carlo algorithm first invented by lal which generates self avoiding walks saws in a canonical fixed n ensemble with free endpoints heren is the number of steps in the walk we find that the pivot algorithm is extraordinarily efficient one effectively independent sample can be produced in a computer time of ordern this paper is a comprehensive study of the pivot algorithm including a heuristic and numerical analysis of the acceptance fraction and autocorrelation time an exact analysis of the pivot algorithm for ordinary random walk a discussion of data structures and computational complexity a rigorous proof of ergodicity and numerical results on self avoiding walks in two and three dimensions our estimates for critical exponents are 0 7496 0 0007 ind 2 and 0 592 0 003 ind 3 95 confidence limits based on saws of lengths 200 n 10000 and 200 n 3000 respectively

optimal zero delay jamming over an additive noise channel this paper considers the problem of optimal zero delay jamming over an additive noise channel building on a sequence of recent results on conditions for linearity of optimal estimation and of optimal mappings in source channel coding the saddle point solution to the jamming problem is derived for general sources and channels without recourse to gaussianity assumptions the linearity conditions are shown to play a pivotal role in jamming in the sense that the optimal jamming strategy is to effectively force both the transmitter and the receiver to default to linear mappings i e the jammer ensures whenever possible that the transmitter and the receiver cannot benefit from non linear strategies this result is shown to subsume the known result for gaussian source and channel the conditions and general settings where such unbeatable strategy can indeed be achieved by the jammer are analyzed moreover a numerical procedure is provided to approximate the optimal jamming strategy in the remaining source channel cases where the jammer cannot impose linearity on the transmitter and the receiver next the analysis is extended to vector sources and channels this extension involves a new aspect of optimization the allocation of available transmit and jamming power over source and channel components similar to the scalar setting the saddle point solution is derived using the linearity conditions in vector spaces the optimal power allocation strategies for the jammer and the transmitter have an intuitive interpretation as the jammer allocates power according to water filling over the channel eigenvalues while the transmitter performs water pouring reverse water filling over the source eigenvalues

the critical problem of kirchhoff type elliptic equations in dimension four abstract we study the following kirchhoff type elliptic problem p a b u 2 d x u u q u 3 u 0 in u 0 on where r 4 is a bounded domain with smooth boundary moreover we assume a 0 b 0 and 1 q 3 in this paper we prove the existence of solutions of p our tools are the variational method and the concentration compactness argument for ps sequences

existence and multiplicity of solutions for a superlinear kirchhoff type equations with critical sobolev exponent in r n abstract in this article we consider a class of superlinear kirchhoff type equations with critical growth a b r n u 2 d x u u 2 1 k x u q 1 x r n u d 1 2 r n where 0 n 4 2 q 2 2 2 n n 2 a b 0 and a b 0 k satisfies some conditions by using the variational method the multiplicity of positive solutions and infinitely many pairs of solutions are obtained

a priori bounds for positive solutions of kirchhoff type equations abstract let be a bounded smooth domain in r n assume that 0 2 1 2 a 0 and b 0 we consider the following dirichlet problem of kirchhoff type equation 0 1 a b u 2 2 u u p 1 u h x u u in u 0 on with p 0 2 1 where 2 for n 2 and 2 n 2 n 2 for n 3 under suitable conditions of h x u u see a h 1 and h 2 in section 3 we get a priori estimates for positive solutions to problem 0 1 by making use of these estimates and the continuous method we further get some existence results for positive solutions to problem 0 1 when 0 p 1 or 2 1 p 2 effects of the term a b u 2 2 on the solution set of problem 0 1 can be seen in an example given in section 2