quasilinear asymptotically periodic schrodinger equations with subcritical growth abstract in this article the existence of one solution for a class of asymptotically periodic equations in the euclidean space is established the basic tools employed here are the mountain pass theorem and the concentration compactness principle by using a change of variable the quasilinear equation is reduced to a semilinear equation whose respective associated functional is well defined in h 1 r n and satisfies the geometric hypotheses of the mountain pass theorem

existence and stability of standing waves for a planar gauged nonlinear schrodinger equation abstract in this article we prove the existence stability and mass collapse behavior of standing waves for the chern simons schrodinger model in the plane this is a covariant nonlinear schrodinger type problem which is mass critical and arises from the chern simons theory in the defocusing case 1 we prove the existence of stable standing waves with arbitrary mass however in the focusing case 1 stable standing waves with small mass exist and we give a mass collapse behavior of the standing waves

on the local well posedness of quasilinear schrodinger equations in arbitrary space dimension abstract a class of quasilinear schrodinger equations is studied which contain strongly singular nonlinearities including derivatives of second order such equations have been derived as models of several physical phenomena the results of this paper apply to the superfluid film equation in fluid mechanics the local well posedness for smooth solutions of the cauchy problem is proved in arbitrary space dimension without any smallness assumption on the initial value this improves results in the literature which cover the one dimensional case only almost global well posedness results are obtained as well the proof combines nash moser techniques on implicit function theorems in frechet spaces with hyperbolic semigroup theory including evolution systems using the intersection of all sobolev spaces as basic function space the nondissipativity is overcome by a transformation procedure yielding the evolution operator and a priori estimates of higher order sobolev norms for the linearized problem here a certain trace has to vanish in view of apparent integrability conditions the transformations and the regularity theory are substantially different from the easier one dimensional case in particular continuity estimates are proved for the operator norms of the linear evolution operator in negative sobolev spaces

existence of solution for a class of quasilinear schrodinger equation in rn with zero mass abstract in this paper we use variational methods to establish a berestycki lions type result for two classes of quasilinear schrodinger equations in r n in the zero mass situation

multiple solutions to some degenerate quasilinear equation with variable exponents via perturbation method abstract in this paper we prove the existence of signed and sign changing solutions to some degenerate quasilinear and elliptic equation containing a gradient term and involving a variable exponent our main idea is to make use of the perturbation method together with invariant sets of descending flow the fact that the exponent is not constant plays an important role

multiple solutions for quasilinear elliptic equations with a finite potential well abstract we consider multiplicity of solutions for a class of quasilinear problems which has received considerable attention in the past including the so called modified nonlinear schrodinger equations by combining a new variational approach via q laplacian regularization and the compactness arguments from 4 we establish infinitely many bound state solutions for the quasilinear schrodinger type equations extending the earlier work of 4 for semilinear equations

multiple solutions for a quasilinear schrodinger equation abstract in this paper we consider the quasilinear schrodinger equation u v x u u 2 u g x u x r n where g and v are periodic in x 1 x n and g is odd in u subcritical and satisfies a monotonicity condition we employ the approach developed in szulkin and weth 2009 2010 15 16 and obtain infinitely many geometrically distinct solutions

micro and macrodiversity mdpsk on shadowed frequency selective channels the performance of m ary differential phase shift keying mdpsk on frequency selective slow rayleigh fading lognormal shadowed channels with diversity combining is analyzed for mobile and portable applications the use of l branch equal gain postdetection microdiversity combining to mitigate the effects of fading and p port macrodiversity to alleviate the effects of shadowing are investigated four performance criteria are considered for a frequency selective multipath fading intersymbol interference channel these are the short term bit error rate ber the irreducible ber the complementary distribution over the lognormal shadowing of the average ber and the probability that the instantaneous ber exceeds a threshold value averaged over a spatial environment closed form expressions for the four performance criteria are obtained the ber and outage performance results show that diversity combining is an effective method for improving the system performance and hence system reliability when the normalized delay spread is not large it is also seen that in most cases 4dpsk gives the best performance followed by 8dpsk and 2dpsk respectively for a given information throughput

existence of soliton solutions for a quasilinear schrodinger equation involving critical exponent in rn abstract mountain pass in a suitable orlicz space is employed to prove the existence of soliton solutions for a quasilinear schrodinger equation involving critical exponent in r n these equations contain strongly singular nonlinearities which include derivatives of the second order such equations have been studied as models of several physical phenomena the nonlinearity here corresponds to the superfluid film equation in plasma physics

quasilinear elliptic equations with critical growth via perturbation method abstract we consider a class of quasilinear schrodinger equations which include the modified nonlinear schrodinger equations a new perturbation approach is used to treat the critical exponent case giving new existence results

multiplicity of normalized solutions for a class of nonlinear schrodinger poisson slater equations abstract in this paper we prove a multiplicity result of solutions for the following stationary schrodinger poisson slater equations 0 1 u u x 1 u 2 u u p 2 u 0 in r 3 where r is an undetermined parameter and p 10 3 6 we obtain couple solutions u with u having a prescribed l 2 norm our proofs are mainly inspired by a recent work of bartsch and de valeriola 7

normalized solutions for schrodinger poisson equations with general nonlinearities abstract in this paper we prove the existence of normalized solutions to the following schrodinger poisson equation u x 1 u 2 u f u u x r 3 r where f c r r satisfies more general conditions which cover the case f u u q 2 u with q 3 10 3 10 3 6 especially some new analytical techniques are presented to overcome the difficulties due to the presence of three terms in the corresponding energy functional which scale differently

on a nonhomogeneous and singular quasilinear equation involving critical growth in r2 abstract this paper establishes sufficient conditions for the existence and multiplicity of solutions for nonhomogeneous and singular quasilinear equations of the form u v x u u 2 u g x u x a h x in r 2 where a 0 2 v x is a continuous positive potential bounded away from zero and which can be large at infinity the nonlinearity g x s is allowed to enjoy the critical exponential growth with respect to the trudinger moser inequality and the nonhomogeneous term h belongs to l q r 2 for some q 1 2 by combining variational arguments in a nonstandard orlicz space context with a singular version of the trudinger moser inequality we obtain the existence of two distinct solutions when h q is sufficiently small schrodinger equations of this type have been studied as models of several physical phenomena

quasilinear asymptotically periodic elliptic equations with critical growth abstract the existence of a nontrivial solution for a class of asymptotically periodic equations involving the p laplacian operator in the euclidean space is established the solutions are obtained by an application of the mountain pass theorem and the concentration compactness principle the lack of compactness due to the fact that the domain is unbounded is compensated by comparing the minimax level associated with the original problem and the minimax level associated with the periodic limit problem

ground state solutions for generalized quasilinear schrodinger equations without ar condition abstract in this paper we study the following generalized quasilinear schrodinger equations div g 2 u u g u g u u 2 v x u h x u x r n where n 3 g r r is an even differentiable function satisfying lim t g t t 1 0 for some 1 h x t is a given function behaving like t 2 1 at infinity which does not satisfy the a r condition combining the change of variables and the monotone method developed by jeanjean in 16 we obtain the existence of positive ground state solutions for the given problem

infinitely many radial and non radial solutions to a quasilinear schrodinger equation abstract in this paper we are concerned with the following quasilinear schrodinger equation u u u 2 v x u f x u x r n by using a change of variables we obtained the existence of a sequence of radial solutions for n 2 a sequence of nonradial solutions for n 4 or n 6 and a nonradial solution for n 5

positive solution for a quasilinear elliptic equation involving critical or supercritical exponent this paper concerns the quasilinear elliptic equation u u u2 u up 2u uq 2uinrn where n 3 2 0 sufficiently small existence of a positive solution will be proved via variational methods together with truncation technique and l estimate the main novelty is that no growth condition is required for the nonlinearity

the cauchy problem for quasi linear schrodinger equations with x rn t r with x1 xn and summation convention one may think of the equation in 1 1 as a non linear schrodinger equation where the operator modeling the dispersion relation is non isotropic and depends also on the unknown function its conjugate and their gradients in the space variables under appropriate assumptions on the function f the method presented here extends to fully non linear schrodinger equations of the form

soliton solutions for quasilinear schrodinger equations ii abstract for a class of quasilinear schrodinger equations we establish the existence of ground states of soliton type solutions by a variational method

on a class of periodic quasilinear schrodinger equations involving critical growth in r2 abstract we consider the equation u v x u k 2 u 2 u g x u u 0 x r 2 where v r 2 r and g r 2 r r are two continuous 1 periodic functions and k is a positive constant also we assume g behaves like exp u 4 as u we prove the existence of at least one weak solution u h 1 r 2 with u 2 h 1 r 2 the mountain pass in a suitable orlicz space together with the trudinger moser inequality are employed to establish this result such equations arise when one seeks for standing wave solutions for the corresponding quasilinear schrodinger equations schrodinger equations of this type have been studied as models of several physical phenomena the nonlinearity here corresponds to the superfluid film equation in plasma physics

performance of differentially coherent digital communications over frequency selective fading channels the performance of binary differential phase shift keyed dpsk communications over frequency selective wide sense stationary uncorrelated scattering fading channels is considered a technique is described for obtaining bounds on the average error probability for dpsk in terms of one or two parameters obtained from multipath spread or frequency correlation function channel measurements a method of approximating the performance of systems using various data pulse shapes and systems where it is difficult to obtain a complete channel characterization is developed numerical examples and comparisons of the most interesting cases are given

multiplicity of nonnegative solutions for quasilinear schrodinger equations abstract the paper deals with existence and multiplicity of nonnegative weak solutions for quasilinear schrodinger equations involving nonlinearities with possibly supercritical growth at infinity and indefinite sign an appropriate change of variables reduces the quasilinear problem into a semilinear one variational and sub super methods are applied in order to obtain the main results of the paper

critical exponents and solitary wave solutions for generalized quasilinear schrodinger equations abstract this paper is concerned with the solitary wave solutions for a generalized quasilinear schrodinger equation in r n involving critical exponents which have appeared from plasma physics as well as high power ultashort laser in matter we find the related critical exponents for a generalized quasilinear schrodinger equation and obtain its solitary wave solutions by using a change of variables and variational argument

normalized ground states for the nls equation with combined nonlinearities abstract we study existence and properties of ground states for the nonlinear schrodinger equation with combined power nonlinearities u u u q 2 u u p 2 u in r n n 1 having prescribed mass r n u 2 a 2 under different assumptions on q p a 0 and r we prove several existence and stability instability results in particular we consider cases when 2 q 2 4 n p 2 q p i e the two nonlinearities have different character with respect to the l 2 critical exponent these cases present substantial differences with respect to purely subcritical or supercritical situations which were already studied in the literature we also give new criteria for global existence and finite time blow up in the associated dispersive equation

asymptotic uniqueness of ground states for a class of quasilinear schrodinger equations with h 1 supercritical exponent in this paper we obtain the asymptotic uniqueness of ground states for a class of quasilinear schrodinger equations with h1 supercritical exponent to this aim the uniqueness and the non degeneracy of positive solutions of the corresponding limit equation which is a zero mass problem play important roles thus we also show the uniqueness and non degeneracy result for a class of zero mass problems by applying ode techniques

the existence of solutions with prescribed l2 norm for kirchhoff type system in this paper we study the existence of positive solutions with prescribed l2 norm for two component kirchhoff type systems in the whole space under different types of potentials we consider the l2 subcritical case and l2 critical case by the constrained variational method

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

normalized solutions for a coupled schrodinger system with saturable nonlinearities abstract we study the existence of prescribed l 2 norm solutions for the coupled schrodinger system with saturable nonlinearities which appears in models for propagation of a beam with two mutually incoherent components in a bulk saturable medium moreover the standing waves associated to the set of minimizers have the orbital stability

blow up phenomena and asymptotic profiles of ground states of quasilinear elliptic equations with h1 supercritical nonlinearities abstract this paper is concerned with asymptotic profiles of ground states for a class of quasilinear schrodinger equations with h 1 supercritical nonlinearities we study the blow up rate of ground states by using the dual variational structure of equations as well as various variational methods

uniqueness and nondegeneracy of the ground state for a quasilinear schrodinger equation with a small parameter abstract we study least energy solutions of a quasilinear schrodinger equation with a small parameter we prove that the ground state is nondegenerate and unique up to translations and phase shifts using bifurcation theory

global existence of small solutions to a relativistic nonlinear schrodinger equation on etudie le probleme de cauchy associea une equation de schrodinger non lineaire modelisant une impulsion laser ultra intense et ultra courte dans un plasma les termes non lineaires nouveaux sont dus aux effets relativistes et a la force ponderomotrice nous prouvons l existence locale et l unicite de solutions petites lorsque la dimension de l espace transverse est egale a 2 ou 3 ainsi que l existence locale pour des donnees initiales de taille arbitraire en dimension un d espace transverse

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

existence and instability of standing waves with prescribed norm for a class of schrodinger poisson equations in this paper we study the existence and the instability of standing waves with prescribed l norm for a class of schrodinger poisson slater equations in r 0 1 i t x 1 p 2 0 when p 10 3 6 to obtain such solutions we look to critical points of the energy functional f u 1 2 ou 2l2 r3 1 4

performance of binary fsk communications over frequency selective rayleigh fading channels the performance of binary frequency shift keyed communications over frequency selective wide sense stationary uncorrelated scattering rayleigh fading channels is discussed previous analyses of fsk communications over frequency selective channels have considered the average probability of error for specific models for the fading channel and typically assume that the two fsk signals are orthogonal a technique for obtaining bounds on the average error probability for fsk in terms of one or two parameters obtainable from multipath spread or frequency correlation functions channel measurements is described

uniqueness of the ground state solutions of quasilinear schrodinger equations abstract we are concerned with the uniqueness result of positive solutions for a class of quasilinear elliptic equation arising from plasma physics we convert a quasilinear elliptic equation into a semilinear one and show the unique existence of positive radial solution for original equation under the suitable conditions on the power of nonlinearity and quasilinearity we also investigate the non degeneracy of a positive radial solution for a converted semilinear elliptic equation

solutions for a quasilinear schrodinger equation a dual approach abstract we consider quasilinear stationary schrodinger equations of the form 1 u u 2 u g x u x r n introducing a change of unknown we transform the search of solutions u x of 1 into the search of solutions v x of the semilinear equation 2 v 1 1 2f 2 v g x f v x r n where f is suitably chosen if v is a classical solution of 2 then u f v is a classical solution of 1 variational methods are then used to obtain various existence results

normalized standing waves for the hartree equations abstract in this paper we study the existence and stability instability of standing waves with a prescribed l 2 norm for the following hartree equation 0 1 i u t u a x 2 u x u 2 u 0 t x r r n where t is time n 3 0 n and a 0 is a constant to get such solutions we look for normalized solutions of the associated stationary equation 0 2 u a x 2 u u x u 2 u 0 x r n two cases are considered i the system is free a 0 and i i a harmonic trapping potential is added in the system a 0 in case i by constructing a suitable submanifold of a l 2 sphere we prove the existence of a normalized solution for problem 0 2 with least energy in the l 2 sphere which corresponds to a normalized ground state standing wave of problem 0 1 then we show that each normalized ground state of problem 0 2 coincides a ground state of problem 0 2 in the usual sense furthermore we give a global existence result for problem 0 1 and also show that any normalized ground state standing wave is strongly unstable in case i i for small a 0 we prove the existence of two different standing waves one corresponds to a topological local minimizer of the constrained energy functional the other corresponds to a mountain pass type solution of problem 0 2 with its energy strictly larger than that of the normalized ground state moreover we show that the set of normalized ground state solutions for problem 0 2 is stable under the associated flow finally to connect case i and case i i we analyze the asymptotic behavior of the two solutions to problem 0 2 obtained in case i i as the trapping frequency a vanishes

infinitely many sign changing solutions to some quasilinear equation involving exponential term abstract in this paper we prove the existence of infinitely many sign changing solutions to some quasilinear and elliptic equation whose divergence part contains exponential term our main idea consists of the use of the perturbation method together with invariant sets of descending flow in the framework of classical critical point theory

nonnegative solution for quasilinear schrodinger equations that include supercritical exponents with nonlinearities that are indefinite in sign abstract in this study we establish the existence of solutions for quasilinear schrodinger equations involving supercritical growth with nonlinearities that are indefinite in sign by changing the variables the quasilinear equations are reduced to semilinear and variational methods which are then used to obtain existence results

standing wave solutions for generalized quasilinear schrodinger equations with critical growth abstract we study the existence of standing wave solutions for generalized quasilinear schrodinger equations involving critical sobolev exponents we use the variational methods to obtain a nonexistence theorem and two existence results

binary communications through noisy non gaussian channels new and unifying analytical tools are developed and used to evaluate the bit error probability false alarm and detection probabilities that result when binary information is communicated through a random channel further disturbed by additive white gaussian noise the class of channels modeled here are those which envelop the received electric field with an arbitrary space time complex envelope the complex gaussian envelope being a special case yields the rayleigh and rice fading statistics considerable insight into the problem of communicating through a complex non gaussian fading channel is obtained by decomposing the performance measures into the sum of two terms viz one attributable to the usually assumed complex gaussian envelope plus a residual performance term expressed as a series expansion in terms of multidimensional hermite polynomials whose coefficients are the channel quasi moments finally a numerical example is presented in which the theory is applied to a specific non gaussian channel

soliton solutions for quasilinear schrodinger equations with critical growth in this paper we establish the existence of standing wave solutions for quasilinear schrodinger equations involving critical growth by using a change of variables the quasilinear equations are reduced to semilinear one whose associated functionals are well defined in the usual sobolev space and satisfy the geometric conditions of the mountain pass theorem using this fact we obtain a cerami sequence converging weakly to a solution v in the proof that v is nontrivial the main tool is the concentration compactness principle due to p l lions together with some classical arguments used by h brezis and l nirenberg 1983 in 9

existence of solutions to a class of asymptotically linear schrodinger equations in rn via the pohozaev manifold abstract in this study we investigate the nonexistence of a least energy solution and the existence of a positive solution for a class of nonhomogeneous asymptotically linear schrodinger equations in r n via the pohozaev manifold after changing the variables the quasilinear operator becomes a semilinear nonhomogeneous operator the technique used employs variational methods that are constrained to the pohozaev manifold which are combined with the splitting lemma