exponential p convergence analysis for stochastic bam neural networks with time varying and infinite distributed delays we discuss exponential p convergence for stochastic bam neural networks the delays here are multiple time varying and infinite distributed delays we establish a new l operator delay differential integral inequality delay dependent criteria ensuring exponential p convergence are obtained giving the detail estimations of the exponential p convergence ball this paper is concerned with the problem of global exponential p convergence for stochastic bam neural networks with time varying and infinite distributed delays by constructing a new delay differential integral inequality and a novel l operator differential integral inequality and coupling with stochastic analysis techniques some delay dependent sufficient conditions are derived to guarantee exponential p convergence and the state variables of the discussed stochastic bam neural networks are globally exponentially convergent to a ball in the state space with a pre specified convergence rate meanwhile the exponential p convergent balls are also estimated here the existence and the uniqueness of the equilibrium point needs not to be considered finally two examples with numerical simulations are given to illustrate the effectiveness of the theoretical results

boundedness and exponential stability for nonautonomous rcnns with distributed delays some sufficient conditions for the ultimate boundedness and global exponential stability of a class of nonautonomous reaction diffusion cellular neural networks rcnns with distributed delays are obtained by means of the lyapunov functional method without assuming that the activation functions f i j l are bounded the results extend and improve the earlier publications

semiclassical solutions for choquard equations with berestycki lions type conditions abstract this paper is concerned with existence of multiple semiclassical states for a class of choquard equation under the classic berestycki lions type assumptions assumed on the nonlinearity we obtain multiplicity of semiclassical solutions for the equation by using a method of penalization argument we study further the concentration phenomena of such solutions and show that they converge to the least energy solutions of the associated limit problem as the parameter e goes to 0

global exponential stability in dcnns with distributed delays and unbounded activations we study delayed cellular neural networks dcnns whose state variables are governed by nonlinear integrodifferential differential equations with delays distributed continuously over unbounded intervals the networks are designed in such a way that the connection weight matrices are not necessarily symmetric and the activation functions are globally lipschitzian and they are not necessarily bounded differentiable and monotonically increasing by applying the inequality pa p 1b p 1 a p b p where p denotes a positive integer and a b denote nonnegative real numbers and constructing an appropriate form of lyapunov functionals we obtain a set of delay independent and easily verifiable sufficient conditions under which the network has a unique equilibrium which is globally exponentially stable a few examples added with computer simulations are given to support our results

ground state solutions for a choquard equation with lower critical exponent and local nonlinear perturbation abstract this paper deals with the following choquard equation with a local nonlinear perturbation u u i u n 1 u n 1 u f u x r n u h 1 r n where i r n r is the riesz potential n 3 0 n the exponent n 1 is critical with respect to the hardy littlewood sobolev inequality and the nonlinear perturbation f is only required to satisfy some weak assumptions near 0 and our results improve the previous related ones in the literature

singularly perturbed critical choquard equations abstract in this paper we study the semiclassical limit for the singularly perturbed choquard equation e 2 u v x u e 3 r 3 q y g u y x y d y q x g u in r 3 where 0 3 e is a positive parameter v q are two continuous real function on r 3 and g is the primitive of g which is of critical growth due to the hardy littlewood sobolev inequality under suitable assumptions on g we first establish the existence of ground states for the critical choquard equation with constant coefficients next we establish existence and multiplicity of semi classical solutions and characterize the concentration behavior by variational methods

groundstates for a local nonlinear perturbation of the choquard equations with lower critical exponent abstract we prove the existence of ground state solutions by variational methods to the nonlinear choquard equations with a nonlinear perturbation u u i u n 1 u n 1 u f x u in r n where n 1 i is the riesz potential of order 0 n the exponent n 1 is critical with respect to the hardy littlewood sobolev inequality and the nonlinear perturbation f satisfies suitable growth and structural assumptions

ground states and non existence results for choquard type equations with lower critical exponent and indefinite potentials abstract in this paper we study following choquard equation with lower critical exponent u v x u i u n 1 u n 1 u f x u x r n u h 1 r n where n 1 i is the riesz potential and v r n r allows to be sign changing under some mild assumptions imposed on the nonlinearity f we prove that above equation has a ground state solution for the periodic case and asymptotically periodic case respectively the characterization of the ground states is also investigated by a direct approach that are constrained to the nehari manifold moreover we show a non existence result for the equation via a generalized poho aev identity established for the non autonomous nonlinearity f the results extend and improve some recent ones in the literature

further result on asymptotic stability criterion of cellular neural networks with time varying discrete and distributed delays based on a recent work and the linear matrix inequality lmi optimization approach we extend the recent work on global asymptotic stability of a class of neural networks to uncertain cellular neural networks with time varying discrete and distributed delays

ground state and bounded state solution for the nonlinear fractional choquard schrodinger poisson system in this paper we study a class of fractional choquard schrodinger poisson system under some suitable assumptions by using a variational approach we establish the existence of non negative ground state solution and also discuss the nonexistence of ground states moreover we prove the existence of bounded state by using a linking theorem

multiplicity and concentration results for fractional choquard equations doubly critical case abstract in this paper we consider the following fractional choquard equation e 2 s s u v x u e i f u f u x r n where n 3 s 0 1 and 0 n e 0 is a parameter i is the riesz potential and f u 1 2 u 2 1 2 u 2 where 2 n n and 2 n n 2 s are lower and upper critical exponents in the sense of the hardy littlewood sobolev inequality firstly by the refined sobolev inequality with morrey norm we show a generalization of lions type theorem secondly combining this theorem with variational methods we show the multiplicity and concentration of positive solutions for above equation moreover the multiplicity and concentration results are obtained in the case where f u has the lower critical exponent 2 which remains unsolved in the existing literature

on the classification of the spectrally stable standing waves of the hartree problem abstract we consider the fractional hartree model with general power non linearity and arbitrary spatial dimension we construct variationally the normalized solutions for the corresponding choquard pekar model in particular a number of key properties like smoothness and bell shapedness are established as a consequence of the construction we show that these solitons are spectrally stable as solutions to the time dependent hartree model in addition we analyze the spectral stability of the moroz van schaftingen solitons of the classical hartree problem in any dimensions and power non linearity a full classification is obtained the main conclusion of which is that only and exactly the normalized solutions which exist only in a portion of the range are spectrally stable

the existence of least energy nodal solutions for some class of kirchhoff equations and choquard equations in r n abstract in this paper we study the existence of least energy nodal solutions for a class of kirchhoff type problems in r n since the kirchhoff equation is a nonlocal one the variational setting to look for sign changing solutions is different from the local cases by using constrained minimization on the sign changing nehari manifold we prove the kirchhoff problem has a least energy nodal solution with its energy exceeding twice the least energy as a co product of our approaches we obtain the existence of least energy sign changing solution for choquard equations in r n and show that the sign changing solution has an energy strictly larger than the least energy and less than twice the least energy

global exponential stability analysis on impulsive bam neural networks with distributed delays using m matrix and topological degree tool sufficient conditions are obtained for the existence uniqueness and global exponential stability of the equilibrium point of bidirectional associative memory bam neural networks with distributed delays and subjected to impulsive state displacements at fixed instants of time by constructing a suitable lyapunov functional the results remove the usual assumptions that the boundedness monotonicity and differentiability of the activation functions it is shown that in some cases the stability criteria can be easily checked finally an illustrative example is given to show the effectiveness of the presented criteria

periodic oscillatory solution of bidirectional associative memory networks with delays periodic oscillatory phenomena of bidirectional associative memory bam networks with axonal signal transmission delays are investigated by constructing suitable lyapunov functionals and some analysis techniques some simple sufficient conditions are derived ensuring the existence and uniqueness of periodic oscillatory solutions of the bam with delays and all other solutions of the bam converge exponentially to a periodic oscillatory solution these conditions are presented in terms of system parameters and have an important leading significance in the design and applications of periodic oscillatory neural circuits for the bam with delays

on nonlocal choquard equations with hardy littlewood sobolev critical exponents abstract we consider the following nonlinear choquard equation with dirichlet boundary condition u u 2 x y d y u 2 2 u f u in where is a smooth bounded domain of r n 0 n 3 0 n and 2 is the critical exponent in the sense of the hardy littlewood sobolev inequality under suitable assumptions on different types of nonlinearities f u we are able to prove some existence and multiplicity results for the equation by variational methods

ground state solutions for a class of choquard equations with potential vanishing at infinity abstract this paper is dedicated to studying the following nonlinear choquard equation u v x u r n q y f u y x y d y q x f u u d 1 2 r n where n 3 0 n v c r n 0 q c r n 0 f c r r and f t 0 t f s d s by combining the non nehari manifold approach with some new inequalities we prove that the above equation has a ground state solution in the case when v x 0 as x where the strict monotonicity condition on f is not required moreover by using perturbation method we obtain the existence of a least energy solution in the zero mass case i e v 0 where f satisfies the condition that f t 0 0 for some t 0 r instead of the usual ambrosetti rabinowitz type condition these results extend the ones in alves figueiredo and yang 2015 1 and some related literature

global asymptotic stability of reaction diffusion cohen grossberg neural networks with continuously distributed delays this paper is concerned with the global asymptotic stability of a class of reaction diffusion cohen grossberg neural networks with continuously distributed delays under some suitable assumptions and using a matrix decomposition method we apply the linear matrix inequality lmi method to propose some new sufficient stability conditions for the reaction diffusion cohen grossberg neural networks with continuously distributed delays the obtained results are easy to check and improve upon the existing stability results some remarks are given to show the advantages of the obtained results over the previous results an example is also given to demonstrate the effectiveness of the obtained results

classification of positive solitary solutions of the nonlinear choquard equation in this paper we settle the longstanding open problem concerning the classification of all positive solutions to the nonlinear stationary choquard equation delta u u 2u left frac 1 x u 2 right 0 quad u in h 1 mathbb r 3 which can be considered as a certain approximation of the hartree fock theory for a one component plasma as explained in lieb and lieb simon s papers starting from 1970s we first prove that all the positive solutions of this equation must be radially symmetric and monotone decreasing about some fixed point interestingly to use the new method of moving planes introduced by chen li ou we deduce the problem into an elliptic system as a key step we transform this differential system into a system of integral equations with the help of riesz and bessel potentials and then use the method of a moving plane in an integral form next using radial symmetry we deduce the uniqueness result from lieb s work our argument can be adapted well to study the radial symmetry of positive solutions of the equation in the generalized form u k 1 f left u k 2 u right

existence of positive solutions for a class of quasilinear schrodinger equations of choquard type abstract in this paper we study the following quasilinear schrodinger equation of choquard type u v x u u 2 u i u p u p 2 u x r n where n 3 0 n 2 n n p 2 n n 2 and i is a riesz potential under appropriate assumptions on v x we establish the existence of positive solutions

existence and concentration of ground state solutions for a critical nonlocal schrodinger equation in r2 we study the following singularly perturbed nonlocal schrodinger equation e2 u v x u e 2 1 x f u f u inr2 where v x is a continuous real function on r2 f s is the primitive of f s 0 2 and e is a positive parameter assuming that the nonlinearity f s has critical exponential growth in the sense of trudinger moser we establish the existence and concentration of solutions by variational methods

general criteria for asymptotic and exponential stabilities of neural network models with unbounded delays abstract for a family of differential equations with infinite delay we give sufficient conditions for the global asymptotic and global exponential stability of an equilibrium point this family includes most of the delayed models of neural networks of cohen grossberg type with both bounded and unbounded distributed delay for which general asymptotic and exponential stability criteria are derived as illustrations the results are applied to several concrete models studied in the literature and a comparison of results is given

existence and nonexistence results for kohn laplacian with hardy littlewood sobolev critical exponents abstract in this article we are study the following dirichlet problem with choquard type non linearity h u a u u q 1 d u q 2 u in u 0 on where is a smooth bounded subset of the heisenberg group h n n n with c 2 boundary and h is the kohn laplacian on the heisenberg group h n here q 2 q q 2 q 2 n 2 and a is a positive real parameter we derive the brezis nirenberg type result for the above problem moreover we also prove the regularity of solutions and nonexistence of solutions depending on the range of a

multiplicity and concentration of solutions for choquard equations with critical growth abstract in this paper we are concerned with the choquard equation 2 u v x u 3 r 3 u y 6 q y f u y x y d y u 4 u q x f u 6 in r 3 where 0 is a parameter 0 3 6 is the critical exponent in the sense of hardy littlewood sobolev inequality in r 3 v and q are bounded continuous functions f is a continuous subcritical term and f is the primitive function of f by variational methods we establish the existence and concentration of positive ground states and investigate the relation between the number of solutions and the topology of the set where v attains its global minimum and q attains its global maximum

an approach to symmetrization via polarization we prove that the steiner symmetrization of a function can be approximated in l p r n by a sequence of very simple rearrangements which are called polarizations this result is exploited to develop elementary proofs of many inequalities including the isoperimetric inequality in euclidean space in this way we also obtain new symmetry results for solutions of some varia tional problems furthermore we compare the solutions of two boundary value problems one of them having a polarized geometry and we show some point wise inequalities between the solutions this leads to new proofs of well known functional inequalities which compare the solutions of two elliptic or parabolic problems one of them having a steiner symmetrized geometry the method also allows us to investigate the case of equality in the inequalities roughly speaking we prove that the equality sign is valid only if the original problem has the symmetrized geometry

on the kirchhoff type choquard problem with hardy littlewood sobolev critical exponent abstract in this paper we study the following kirchhoff type choquard problem 0 1 a b r n u 2 d x u u r n f u y u y 2 x y d y f u 2 u 2 2 u in r n where n 3 a b 0 are constants 0 is a parameter when 0 4 under suitable conditions on b and f we prove that 0 1 has a ground state solution when 4 we also obtain some related existence results

critical fractional p kirchhoff type problem with a generalized choquard nonlinearity in this article based on the concentration compactness principle and the mountain pass theorem we establish the existence of positive solutions to the fractional p kirchhoff type problem with a generalized choquard nonlinearity and a critical hardy sobolev term

exponential stability for stochastic reaction diffusion bam neural networks with time varying and distributed delays abstract in this paper we study the stability for a class of stochastic bidirectional associative memory bam neural networks with reaction diffusion and mixed delays the mixed delays considered in this paper are time varying and distributed delays based on a new lyapunov krasovskii functional and the poincare inequality as well as stochastic analysis theory a set of novel sufficient conditions are obtained to guarantee the stochastically exponential stability of the trivial solution or zero solution the obtained results show that the reaction diffusion term does contribute to the exponentially stabilization of the considered system moreover two numerical examples are given to show the effectiveness of the theoretical results

global exponential periodicity of a class of bidirectional associative memory networks with finite distributed delays in this paper we study the periodic oscillatory behavior of a class of bidirectional associative memory bam networks with finite distributed delays a set of criteria are proposed for determining global exponential periodicity of the proposed bam networks which assume neither differentiability nor monotonicity of the activation function of each neuron in addition our criteria are easily checkable

on a class of hamiltonian choquard type elliptic systems this paper is concerned with the existence of solutions for a class of hamiltonian choquard type elliptic systems in the plane with exponential critical growth typical features of this class of problems are a lack of compactness because of the unboundedness of the domain and that the critical growth and the energy functional associated with this class of systems are strongly indefinite that is the domain has a saddle point geometry where both positive and negative subspaces of the quadratic form are infinite dimensional moreover the presence of the nonlocal term in the nonlinearity provides a series of difficulties in obtaining certain estimates

existence and exponential stability of almost periodic solution for bam neural networks with variable coefficients and delays by using exponential dichotomy the banach fixed point theory constructing suitable lyapunov functional and combining yang inequality some sufficient conditions are derived ensuring existence globally exponential stability of almost periodic solution for bam neural networks with variable coefficients and delays without assuming the boundedness of signal function these results obtained are significant in design and applications of bam neural networks we extend and improve previously known results

multiple normalized solutions for quasi linear schrodinger equations abstract in this paper we prove the existence of two solutions having a prescribed l 2 norm for a quasi linear schrodinger equation one of these solutions is a mountain pass solution relative to a constraint and the other one a minimum either local or global to overcome the lack of differentiability of the associated functional we rely on a perturbation method developed in 25

comments on existence conditions of positive definite solutions for algebraic matrix riccati equations abstract it is pointed out that the main results in a recent paper by kano 1987 have previously been published in the literature

groundstates of nonlinear choquard equations existence qualitative properties and decay asymptotics we consider a semilinear elliptic problem delta u u i alpha ast abs u p abs u p 2 u quad text in r n where i alpha is a riesz potential and p 1 this family of equations includes the choquard or nonlinear schr odinger newton equation for an optimal range of parameters we prove the existence of a positive groundstate solution of the equation we also establish regularity and positivity of the groundstates and prove that all positive groundstates are radially symmetric and monotone decaying about some point finally we derive the decay asymptotics at infinity of the groundstates

stability in impulsive cohen grossberg type bam neural networks with distributed delays in this paper a class of impulsive cohen grossberg type bi directional associative memory bam neural networks with distributed delays is investigated by establishing an integro differential inequality with impulsive initial conditions and employing the homeomorphism theory the m matrix theory and inequality technique some new general sufficient conditions ensuring the existence uniqueness and global exponential stability of equilibrium point for impulsive cohen grossberg type bam neural networks with distributed delays are obtained in particular the estimate of the exponential convergence rate is also provided which depends on the system parameters and impulsive disturbed intension an example is given to show the effectiveness of the results obtained here

existence of groundstates for a class of nonlinear choquard equations we prove the existence of a nontrivial solution h n to the nonlinear choquard equation i in n where i is a riesz potential under almost necessary conditions on the nonlinearity in the spirit of berestycki and lions this solution is a groundstate if moreover is even and monotone on 0 then is of constant sign and radially symmetric

exponential stability and oscillation of hopfield graded response neural network both exponential and stochastic stabilities of the hopfield neural network are analyzed the results are especially useful for analyzing the stabilities of asymmetric neural networks a constraint on the connection matrix has been found under which the neural network has a unique and exponentially stable equilibrium given any connection matrix this constraint can be satisfied through the adjustment of the gains of the amplifiers and the resistances in the neural net circuit a one to one and smooth map between input currents and the equilibria of the neural network can be set up the above results can be applied to the master slave net to prove that the master net can find the best connection matrix for the slave net for the neural network disturbed by some noise the stochastic stability of the network is also analyzed a special asymmetric neural network formed by a closed chain of formal neurons is also studied for its stability and oscillation both stable and oscillatory dynamics are obtained in the closed chain network through the adjustment of the gains and resistances of the amplifiers

global asymptotic stability of bi directional associative memory networks with distributed delays in this paper several sufficient conditions are derived for the global asymptotic stability in bi directional associative memory bam networks with distributed delays by constructing suitable lyapunov functional and the young inequality technique these conditions have an important leading significance in the design and applications of globally asymptotically stable neural circuits for bam with distributed delays

exponential stability and periodic oscillatory solution in bam networks with delays both exponential stability and periodic oscillatory solution of bidirectional associative memory bam networks with axonal signal transmission delays are considered by constructing suitable lyapunov functional and some analysis techniques some simple sufficient conditions are given ensuring the global exponential stability and the existence of periodic oscillatory solutions of bam with delays these conditions are presented in terms of system parameters and have important leading significance in the design and applications of globally exponentially stable and periodic oscillatory neural circuits for bam with delays in addition two examples are given to illustrate the results

existence of a ground state solution for choquard equation with the upper critical exponent abstract in this paper we investigate the following choquard equation u u i u n n 2 u n n 2 2 u g u in r n where n 3 0 n i is the riesz potential and g is a given function if g satisfies the general subcritical growth conditions we obtain the existence of a positive ground state solution

existence and concentration of ground state solutions for choquard equations involving critical growth and steep potential well abstract in the present paper we are interested in the following choquard type equation u v x u i u 2 u 2 2 u u p 2 u in r 3 where p 4 6 r r is a constant such that the operator l v x is non degenerate i is a riesz potential of order 0 3 2 3 is the upper critical exponent due to the hardy littlewood sobolev inequality the function v c r 3 r is nonnegative and has a potential well int v 1 0 additionally the operator has a sequence of dirichlet eigenvalues in h 0 1 expressed as 0 1 2 n n if 1 via the nehari manifold techniques and the ekeland variational principle we prove the existence and concentration of positive ground state solutions for sufficiently large if 1 and j for all j n employing the nehari pankov manifold methods and the constrained minimization arguments we obtain the existence of ground state solution for large enough and verify the asymptotic behaviour of ground state solutions as

on the exponential stability and periodic solutions of delayed cellular neural networks a set of criteria is presented for the global exponential stability and the existence of periodic solutions of delayed cellular neural networks dcnns by constructing suitable lyapunov functionals introducing many parameters and combining with the elementary inequality technique these criteria have important leading significance in the design and applications of globally stable dcnns and periodic oscillatory dcnns in addition earlier results are extended and improved other results are contained two examples are given to illustrate the theory

an analysis on the global exponential stability and the existence of periodic solutions for non autonomous hybrid bam neural networks with distributed delays and impulses in this paper by utilizing the lyapunov functional method applying m matrix young inequality technique and other analysis techniques we analyze the exponential stability and the existence of periodic solutions for non autonomous hybrid bam neural networks with distributed delays and impulses sufficient conditions are obtained for the global exponential stability and the existence of periodic solutions for non autonomous hybrid bidirectional associative memory bam neural networks with lipschitzian activation functions without assuming their boundedness monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time finally two examples are also provided to demonstrate the effectiveness of the results obtained

solutions for a class of quasilinear choquard equations with hardy littlewood sobolev critical nonlinearity abstract in this article we consider the quasilinear choquard equation with critical nonlinearity in r n e 2 u v x u e 2 u u 2 r n u 2 2 x y d y u 2 2 2 u h x u u where 0 n n 3 2 2 n n 2 is the critical exponent in the sense of hardy littlewood sobolev inequality e is a real parameter by using a change of variables the quasilinear equations are reduced to a semilinear one whose associated functionals are well defined in the usual sobolev space and satisfy the geometric conditions of the mountain pass theorem under suitable assumptions on v and h we investigate the existence and multiplicity of solutions for the above problem by using the mountain pass theorem and index theory in order to overcome the lack of compactness we apply the concentration compactness principle