exact analysis of multihop amplify and forward relaying systems over general fading links a new theoretical method the generalized transformed characteristic function gtcf approach gives an exact integral solution for the probability density function of the end to end received signal to noise ratio in multihop amplify and forward relaying systems in turn the gtcf approach is used to obtain exact integral solutions for the ergodic capacity outage probability and average symbol error probability of multihop amplify and forward relaying systems the results are precise for any number of hops and can accommodate any channel fading distribution the theory provides the first exact theoretical solutions for numbers of hops larger than 2

an algebraic approximation for the matrix exponential in singularly perturbed boundary value problems a symmetric difference scheme for linear stiff or singularly perturbed boundary value problems of first order with constant coefficients is constructed being based on a stability function containing a matrix square root its essential feature is the unconditional stability in the absence of purely imaginary eigenvalues of the coefficient matrix local damping of errors uniform stability and uniform second order convergence are proved the computation of the specific matrix square root by a well known stable variant of newton s method is discussed a numerical example confirming the results 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

infinitely many solutions for a differential inclusion problem in r n abstract in this paper we consider the differential inclusion problem di p u u p 2 u x f u x x r n u w 1 p r n where 2 n p l 1 r n l r n is radially symmetric and f stands for the generalized gradient of a locally lipschitz function f r r under suitable oscillatory assumptions on the potential f at zero or at infinity we show the existence of infinitely many radially symmetric solutions of di no symmetry requirement on f is needed our approach is based on a non smooth ricceri type variational principle developed by marano and motreanu j differential equations 182 2002 108 120

existence of a positive solution to kirchhoff type problems without compactness conditions abstract the existence of a positive solution to a kirchhoff type problem on r n is proved by using variational methods and the new result does not require usual compactness conditions a cut off functional is utilized to obtain the bounded palais smale sequences

perturbation bounds for matrix square roots and pythagorean sums abstract perturbation estimates for the square root r a 1 2 and pythagorean sum p i a 2 1 2 of complex matrices are proved we present bounds in the spectral norm for the cases that r and p are accretive i e have positive definite hermitian parts with special attention to the case of a large condition of a the results are based on bounds for the solution of the matrix sylvester equation and for the separation of two matrices

high energy solutions of systems of kirchhoff type equations in rn in the present paper five new critical point theorems on the product spaces are given and three existence theorems for the sequence of high energy solutions for the systems of kirchhoff type equations are studied

infinitely many small solutions for the kirchhoff equation with local sublinear nonlinearities abstract we study the following nonlinear kirchhoff equation on the whole space 1 b r 3 u 2 v x u 2 d x u v x u f x u in r 3 where b 0 is a constant and the nonlinear term f x u is only locally defined for u small and satisfies some mild conditions it is proved that the above problem admits infinity many weak solutions provided that some additional assumptions are satisfied moreover we show that these solutions tend to zero in l r 3 our method relies upon a variant of the symmetric mountain pass lemma due to kajikiya and moser iteration method

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

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

kirchhoff systems with dynamic boundary conditions abstract we are interested in the study of the global non existence of solutions of hyperbolic nonlinear problems governed by the p kirchhoff operator under dynamic boundary conditions when p p n with p n 2 the systems involve nonlinear external forces and may be affected by a perturbation of the type u p 2 u several models already treated in the literature are covered in special subcases and concrete examples are provided for the source term f and the external nonlinear boundary damping q

variational methods for non differentiable functionals and their applications to partial differential equations the interest in extending the theory of nonlinear partial differential equations pde to pde with discontinuous nonlinearities dnde has been increasing daily the reasons are twofold 1 many free boundary problems may be reduced to boundary value problems of dnde cf chang 16 71 chang and jiang 9 and fleishman and mahar 121 2 sometimes in dealing with a pde problem it is beneficial to put the original pde into a large category for instance dnde cf chang 7 simply speaking a dnde is as follows

newton s method for the matrix square root one approach to computing a square root of a matrix a is to apply newton s method to the quadratic matrix equation f x x2 a 0 two widely quoted matrix square root iterations obtained by rewriting this newton iteration are shown to have excellent mathematical convergence properties however by means of a perturbation analysis and supportive numerical examples it is shown that these simplified iterations are numerically unstable a further variant of newton s method for the matrix square root recently proposed in the literature is shown to be for practical purposes numerically stable

infinitely many solutions for a differential inclusion problem in rn involving the p x laplacian abstract in this paper we consider the differential inclusion problem in r n involving the p x laplacian of the type div u p x 2 u u p x 2 u f x u in r n u w 1 p x r n we prove the existence of infinitely many radially symmetric solutions of the problem under suitable hypotheses by applying a nonsmooth variational principle due to marano and motreanu and the theory of the variable exponent sobolev spaces

the existence of radial solutions for differential inclusion problems in rn involving the p x laplacian abstract in this paper we consider a differential inclusion in r n involving a p x laplacian of the type p p x u e x u p x 2 u j x u x in r n u w 1 p x r n where p r n r is a continuous function satisfying some given assumptions the approach used in this paper is the variational method for locally lipschitz functions more precisely on the basis of the weierstrass theorem and the mountain pass theorem we prove that there exist at least two nontrivial solutions when p finally we obtain the existence of at least one nontrivial solution when p

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

global nonexistence for nonlinear kirchhoff systems in this paper we consider the problem of non continuation of solutions of dissipative nonlinear kirchhoff systems involving the p x laplacian operator and governed by nonlinear driving forces f f t x u as well as nonlinear external damping terms q q t x u u t both of which could significantly dependent on the time t the theorems are obtained through the study of the natural energy eu associated to the solutions u of the systems thanks to a new approach of the classical potential well and concavity methods we show the nonexistence of global solutions when the initial energy is controlled above by a critical value that is when the initial data belong to a specific region in the phase plane several consequences interesting in applications are given in particular subcases the results are original also for the scalar standard wave equation when p 2 and even for problems linearly damped

three solutions for a differential inclusion problem involving the p x laplacian abstract in this paper we consider differential inclusion problem involving the p x laplacian of the type div u p x 2 u f x u in u 0 on applying a version of the non smooth three critical points theorem we obtain the existence of three solutions of the problem in w 0 1 p x

multiplicity of solutions for p x polyharmonic elliptic kirchhoff equations abstract in this paper we establish the existence of an unbounded sequence of solutions for a class of quasilinear elliptic p x polyharmonic kirchhoff equations including the new delicate degenerate case not yet covered in the literature the main tool is the symmetric mountain pass theorem of ambrosetti and rabinowitz

exact analysis of dual hop af maximum end to end snr relay selection new exact closed form expressions are derived for the probability density function and the cumulative distribution function of the end to end signal to noise ratio snr of opportunistic dual hop amplify and forward af relaying systems with relay selection the expressions are used to obtain the first exact integral solutions for the ergodic capacity and average symbol error probability and the first exact closed form solution for outage probability of an opportunistic af relaying system where the best node is selected from a number of candidate intermediate nodes to relay the data signal between the source and the destination the selection follows a maximum end to end snr policy based on the available channel state information the results are precise for any number of candidate relays and rayleigh nakagami m or rician fading distributions the effects of different channel fading parameters and the number of relays in the relay selection pool are studied the system performance is compared to that of dual hop af systems without relay selection and to dual hop af relaying systems with maximum relay to destination snr relay selection the adopted selection method provides diversity gain over dual hop af relaying systems without relay selection and over maximum relay to destination snr relay selection the diversity gain is proportional to the relay selection pool size

existence of nonzero weak solutions for a class of elliptic variational inclusions systems in rn abstract we consider the following variational inclusions system of the form u u 1 f u v in r n v v 2 f u v in r n with u v h 1 r n where 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 various growth conditions on the nonlinearity f we study the existence of nonzero weak solutions of the above system in the sense of hemivariational inequalities which are critical points of an appropriate locally lipschitz function defined on h 1 r n h 1 r n the main tool used in the paper is the principle of symmetric criticality for locally lipschitz functions

finite dimensional attractors for the kirchhoff models with critical exponents the paper studies the existence of the finite dimensional global attractor and exponential attractor for the dynamical system associated with the kirchhoff models utt u m 1 u ut 2u h ut g u f x it proves that for the subcritical and critical cases 1 m n 2 n 2 with n 6 the above mentioned dynamical system possesses in phase spaces x1 a finite dimensional global attractor and a weak exponential attractor respectively

bounds for multihop relayed communications in nakagami m fading we present closed form lower bounds for the performance of multihop transmissions with nonregenerative relays over not necessarily identically distributed nakagami m fading channels the end to end signal to noise ratio is formulated and upper bounded by using an inequality between harmonic and geometric means of positive random variables rvs novel closed form expressions are derived for the moment generating function the probability density function and the cumulative distribution function of the product of rational powers of statistically independent gamma rvs these statistical results are then applied to studying the outage probability and the average bit error probability for phase and frequency modulated signaling numerical examples compare analytical and simulation results verifying the tightness of the proposed bounds