multiple nodal bound states for a quasilinear schrodinger equation nehari techniques are used to prove the existence of multiple indeed infinitely many nodal type bound states for the quasilinear schrodinger equation izt v0z z q x z 2z k z 2 z 0 with prescribed number of nodes

periodic solutions of the lienard equation with one sided growth restrictions in this article we are concerned with the problem of the existence of periodic solutions to the periodically forced scalar lienard equation x f x x g x e t d dt 1 where f g e r r are continuous functions and e is periodic we are looking for solutions of 1 having the same period of the forcing term e throughout the paper we assume without loss of generality see e g 22 36 p 693 that

quasilinear elliptic equations involving the n laplacian with critical exponential growth in rn abstract this paper shows the existence of nontrivial solutions for the quasilinear equations of the form n u v x u n 2 u n u 2 u h u in r n where n is the n laplacian operator v is a continuous function bounded from below away from zero and h u is a continuous function having critical exponential growth

multiplicity of solutions for singular quasilinear schrodinger equations with critical exponents abstract by variational methods we study the existence of multiplicity of solutions for singular quasilinear schrodinger equations

existence and uniqueness of periodic solutions for forced rayleigh type equations in this paper we use the coincidence degree theory to establish new results on the existence and uniqueness of t periodic solutions for a kind of forced rayleigh equation of the formx f x t g t x t e t

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

soliton solutions for quasilinear schrodinger equations the critical exponential case abstract quasilinear elliptic equations in r 2 of second order with critical exponential growth are considered by using a change of variable the quasilinear equations are reduced to semilinear equations whose respective associated functionals are well defined in h 1 r 2 and satisfy the geometric hypotheses 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 p l lions the concentration compactness principle in the calculus of variations the locally compact case part i and ii ann inst h poincare anal non lineaire 1 1984 109 145 223 283 combined with test functions connected with optimal trudinger moser inequality

multiple solutions for a class of singular quasilinear problems abstract in this paper we use sub supersolution and minimax methods to show the existence and multiplicity of solutions for the following class of singular quasilinear problems u u 2 u a x u h x u in u 0 in u 0 on where is a bounded smooth domain of r n n 3 the function a x is nonnegative 0 is a constant and the nonlinearity h x u is continuous in our first result the nonlinearity h has an arbitrary polynomial growth and we obtain the existence of a solution for the problem via sub supersolution method for the second result h has subcritical growth and we show the existence of a second solution by applying the mountain pass theorem

semiclassical ground states for quasilinear schrodinger equations with three times growth abstract in this paper we study the quasilinear schrodinger equation 2 u v x u 2 u u 2 q x u 3 u h 1 r 3 where 0 is a parameter v and q are positive bounded functions for the equation with three times growth we establish the existence of ground states for small using the method of nehari manifold we also describe the concentration phenomena of ground states as 0

positive solutions for a class of singular quasilinear schrodinger equations with critical sobolev exponent abstract we prove the existence of positive solutions of the following singular quasilinear schrodinger equations at critical growth u c x u u 2 u 2 2 u u q 2 u u 2 2 u u d 1 2 r n via variational methods where 0 c r n r 0 0 1 2 2 q 2 it is interesting that we do not need to add a weight function to control u q 2 u

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

periodic solutions of rayleigh equations via time maps abstract in this paper we study the existence of periodic solutions of rayleigh equations x f t x g x e t where f r 2 r is continuous and t periodic with respect to the first variable g e r r are continuous and e is t periodic we prove that the given equation possesses at least one t periodic solution provided that either lim sup c c lim inf c c t or lim inf c c lim sup c c t is satisfied where is the time map defined in section 1

a continuation lemma and its applications to periodic solutions of rayleigh differential equations with subquadratic potential conditions in this paper we study the existence of periodic solutions of rayleigh equations x f t x g x e t where f g e are continuous functions and f is t periodic with the first variable e is t periodic by developing a continuation lemma for rayleigh equations we prove that the given equation has at least one t periodic solution provided that f t y is sublinear with respect to the variable y and g x 0xg u du satisfies some subquadratic conditions

multiple solutions for quasilinear schrodinger equations involving critical exponent by using lions second concentration compactness principle and concentration compactness principle at infinity to prove that the ps condition holds locally and by minimax methods and the krasnoselski genus theory we establish the multiplicity of solutions for a class of quasilinear schrodinger equations arising from physics

infinitely many small solutions for a modified nonlinear schrodinger equations abstract in the present paper we study the modified nonlinear schrodinger equations mnse without any growth condition on the nonlinear term we obtain the existence of infinitely many small solutions for mnse by a dual approach

bifurcations for quasilinear schrodinger equations i abstract this paper is concerned with bifurcation problems for quasilinear schrodinger type equations such as the modified nonlinear schrodinger equations which have appeared as several models from mathematical physics we give a new approach for dealing with bifurcation problems of nonlinear potential operators the novelty of our approach lies in establishing multiple bifurcations without making a reduction to finite dimensional problems the finite dimensional reduction procedures that have been used in the past work for semilinear problems but are not suitable for quasilinear problems we give a unified approach requiring much less regularity of the problems as applications we provide multiple bifurcation results for the modified nonlinear schrodinger equations

existence of positive solutions for a class of quasilinear schrodinger equations on rn abstract in this paper we study the following quasilinear schrodinger equation of the form u v x u 1 2 u 2 u u p 1 u u q 1 u x r n where n 3 2 2 n q p 2 2 n n 2 1 r n under appropriate assumptions on v x we establish the existence of ground state solutions by a minimization argument

existence of ground state sign changing solutions for a class of generalized quasilinear schrodinger maxwell system in r3 abstract in this paper we study the existence of ground state sign changing solutions for the following generalized quasilinear schrodinger maxwell system d i v g 2 u u g u g u u 2 v x u g u g u k x f u x r 3 g 2 u x r 3 where g c 1 r r v x and k x are positive continuous functions and is a positive parameter by making a change of variable as u g 1 v and g u 0 u g t d t we obtain one ground state sign changing solution v g 1 u by using some new analytical skills and non nehari manifold method furthermore the energy of v g 1 u is strictly larger than twice that of the ground state solutions of nehari type we also establish the convergence property of v g 1 u as the parameter 0 our results improve and generalize some results obtained by chen and tang 2016 zhu et al 2016

existence of radial bounded solutions for some quasilinear elliptic equations in rn abstract we study the quasilinear equation p div a x u u p 2 u 1 p a t x u u p u p 2 u g x u i n r n with n 3 p 1 where a x t a t x t a t x t and g x t are caratheodory functions on r n r suitable assumptions on a x t and g x t set off the variational structure of p and its related functional j is c 1 on the banach space x w 1 p r n l r n in order to overcome the lack of compactness we assume that the problem has radial symmetry then we look for critical points of j restricted to x r subspace of the radial functions in x following an approach which exploits the interaction between x and the norm on w 1 p r n we prove the existence of at least one weak bounded radial solution of p by applying a generalized version of the ambrosetti rabinowitz mountain pass theorem

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

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

arithmetic brownian motion subordinated by tempered stable and inverse tempered stable processes abstract in the last decade the subordinated processes have become popular and have found many practical applications therefore in this paper we examine two processes related to time changed subordinated classical brownian motion with drift called arithmetic brownian motion the first one so called normal tempered stable is related to the tempered stable subordinator while the second one to the inverse tempered stable process we compare the main properties such as probability density functions laplace transforms ensemble averaged mean squared displacements of such two subordinated processes and propose the parameters estimation procedures moreover we calibrate the analyzed systems to real data related to indoor air quality

solutions for a class of quasilinear schrodinger equations with critical sobolev exponents in this paper we study a class of quasilinear schrodinger equations involving a critical exponent which arises in plasma physics by using the change of variable and variational approaches combining the concentration compactness principle the existence of a positive solution which has a local maximum point and decays exponentially is obtained

critical points for multiple integrals of the calculus of variations in this paper we deal with the existence of critical points of functional defined on the sobolev space w01 p p 1 by j u int limits omega vartheta x u du dx text where is a bounded open subset of n even for very simple examples in n the differentiability of j u can fail to overcome this difficulty we prove a suitable version of the ambrosetti rabinowitz mountain pass theorem applicable to functionals which are not differentiable in all directions existence and multiplicity of nonnegative critical points are also studied through the use of this theorem

a class of minimization problems related to quasilinear equations abstract for a class of minimization problems related to quasilinear equations we establish the existence and nonexistence of minimizers by a minimization argument and the pohozaev type identity

infinitely many solutions for quasilinear schrodinger equation with critical exponential growth in rn abstract this paper shows the existence of infinitely many solutions for the quasilinear equations of the form 0 1 n u v x u n 2 u n u 2 u k x u q 2 u h u x r n where n u is the n laplacian operator n 3 0 1 q n k l r n n n q and h is an odd continuous function having critical exponential growth the potential function v x c r n and 0 inf x r n v x sup x r n v x using mountain pass theorem and some special techniques we demonstrate that there exists 0 0 such that problem 0 1 admits infinitely many high energy solutions provided that 0 0

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

on the existence of standing wave solutions for a class of quasilinear schrodinger systems abstract in this paper minimax methods in a suitable orlicz space are employed to establish the existence of standing wave solutions for a class of quasilinear schrodinger systems involving subcritical nonlinearities the systems considered here can model an interaction phenomena in plasma physics

existence and nonexistence of positive solutions for a class of generalized quasilinear schrodinger equations involving a kirchhoff type perturbation with critical sobolev exponent in this paper by variational methods we study the existence and nonexistence of positive solutions for a class of generalized quasilinear schrodinger equations involving a kirchhoff type perturbation with critical sobolev exponent in particular the first result is based on the ambrosetti rabinowitz condition moreover the second results are established via the poho aev identity finally the last results are not based on the ambrosetti rabinowitz condition and we use generalized conditions to prove the results

ground states for a class of critical quasilinear coupled superlinear elliptic systems abstract in this work we consider the following class of quasilinear coupled systems u a x u u 2 u g u x u 2 u v x r n v b x v v 2 v h v x v 2 v u x r n where n 3 and a b r n r are positive potentials r n r is a nonnegative continuous function 0 and 2 satisfying 2 2 on the nonlinear terms we assume that g h are in c 1 class which are superlinear functions at infinity and at the origin we deal with nonlinearities g and h being subcritical or critical the coupling term is a subcritical function which is superlinear at infinity our main theorem is stated without the well known ambrosetti rabinowitz condition at infinity using a change of variable we turn the quasilinear coupled system into a nonlinear coupled system where we establish a variational approach based on nehari method

invariant tori and unboundedness for second order differential equations with asymmetric nonlinearities depending on the derivatives abstract in this paper the boundedness and unboundedness of solutions of the oscillator x a x b x x x f x g x p t are discussed under some suitable conditions

a class of quasilinear schrodinger equations with critical or supercritical exponents abstract we study the existence of nontrivial solutions for the following quasilinear schrodinger equations u v x u 2 u 2 u l u x r n where v r n r and l u involves critical or supercritical exponents

generalized quasilinear asymptotically periodic schrodinger equations with critical growth this paper is concerned with the following quasilinear schrodinger equations div g 2 u u g u g u u 2 v x u f x u g u g u 2 2 g u x r n u x 0 x r n where n 3 2 2 n n 2 g u 0 u g t d t and 0 is a parameter by using a change of variable the quasilinear equation is reduced to a semilinear one whose associated functional is well defined in h 1 r n we establish the existence of positive solutions for this problem by using the mountain pass theorem in combination with the concentration compactness principle under appropriate assumptions on v x and f x u recent results from the literature are improved and extended

time dependent dissipation in nonlinear schrodinger systems a coupled nonlinear schrodinger poisson equation is considered which contains a time dependent dissipation function as a specific model of dissipation effects in nonlinear quantum transport theory and other areas the wigner poisson equation associated with this system is derived using conservation and quasiconservation laws and certain growth assumptions for the nonlinearities and the dissipation function global existence of solutions to the cauchy problem of the time dependent schrodinger poisson system is shown both for small attractive case or arbitrary data repulsive case

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

h theorems for the brownian motion on the hyperbolic plane abstract we study h theorems associated with the brownian motion with constant drift on the hyperbolic plane since this random process satisfies a linear fokker planck equation it is easy to show that up to a proper scaling its shannon entropy is increasing over time as a consequence its distribution is converging to a maximum shannon entropy distribution which is also shown to be related to the non extensive statistics in a second part relying on a theorem by shiino we extend this result to the case of tsallis entropies we show that under a variance like constraint the tsallis entropy of the brownian motion on the hyperbolic plane is increasing provided that the non extensivity parameter of this entropy is properly chosen in terms of the drift of the brownian motion

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

existence of solutions for a quasilinear schrodinger equation with vanishing potentials abstract in this paper we investigate the existence of positive solutions for the quasilinear schrodinger equation u v x u u 2 u g u in r n where n 3 g has a quasicritical growth and v is a nonnegative potential which can vanish at infinity

existence and multiplicity of solutions for a class of generalized quasilinear schrodinger equations abstract this paper focuses on the following generalized quasilinear schrodinger equations div g 2 u u g u g u u 2 v x u f x u x r n where n 3 g s r r is a nondecreasing function with respect to s by using a change of variables and variational methods we obtain the existence and multiplicity of nontrivial solutions for the above problem when the nonlinearity is superlinear but does not satisfy the ambrosetti rabinowitz type condition

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

ground state solutions for the quasilinear schrodinger equation abstract this paper is concerned with the quasilinear schrodinger equation u a x 1 u 1 2 u 2 u u p u 0 x r n with a x 0 having a potential well and 4 p 1 2 2 by using the variational method and the concentration compactness method in orlicz space we prove the existence of a ground state solution which localizes near the potential well int a 1 0 for large enough

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

non extensive statistical mechanics and generalized fokker planck equation a non linear generalized fokker planck gfp equation is studied whose exact stationary solutions are the maximum entropy distributions introduced by tsallis in his generalization of statistical mechanics in the case of a constant or linearly varying drift the time dependent solutions of the gfp equation are seen to obey a suitable form of the celebrated h theorem the temporal changes of tsallis entropies are seen to be given in terms of the fisher s information measure particular time dependent solutions of the gfp equation of the maximum tsallis entropy form are obtained

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

sharp condition of global existence for second order derivative nonlinear schrodinger equations in two space dimensions this paper discusses a class of second order derivative nonlinear schrodinger equations which are used to describe the upper hybrid oscillation propagation by establishing a variational problem applying the potential well argument and the concavity method we prove that there exists a sharp condition for global existence and blow up of the solutions to the nonlinear schrodinger equation in addition we also answer the question how small are the initial data the global solutions exist

boundedness of solutions for second order differential equations with asymmetric nonlinearity abstract in this paper we are concerned with the boundedness of all solutions of the second order differential equations x f x a x b x g x p t where a b does not lie on one of the fucik spectrum curves the functions f and g are bounded and p is 2 periodic

multiple solutions to a class of generalized quasilinear schrodinger equations with a kirchhoff type perturbation abstract in this paper we consider a class of generalized quasilinear schrodinger equations with a kirchhoff type perturbation under the assumption that the potential may be vanishing at infinity the existence of both the ground state and the ground state sign changing solutions is established furthermore the behavior of these solutions is studied when the perturbation vanishes it is a surprise that we find an interesting phenomenon about the monotonicity for the quotient function as a byproduct

non autonomous perturbations for a class of quasilinear elliptic equations on r abstract this paper is concerned with the existence of two positive solutions for a class of quasilinear elliptic equations on r involving the p laplacian with a non autonomous perturbation the first solution is obtained as a local minimum in a neighborhood of 0 and the second one by a mountain pass argument the special features of the problem here is the complex structure of the linear part which in particular oblige to work into the space w 1 p r then one faces problems in the convergence of the sequences of derivatives u n u

existence of solutions for a quasilinear schrodinger equation with subcritical nonlinearities abstract in this paper we consider the existence of solutions for the quasilinear schrodinger equation u v x u u 2 u g x u in r n where n 3 and g x u is a superlinear but subcritical function under periodic or asymptotically periodic assumptions on the nonlinearities we prove the existence of bounded states for this equation by the mountain pass theorem

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

nodal soliton solutions for quasilinear schrodinger equations with critical exponent this paper is concerned with constructing nodal radial solutions for quasilinear schrodinger equations in rn with critical growth which have appeared as several models in mathematical physics for any given integer k 0 by using a change of variables and minimization argument we obtain a sign changing minimizer with k nodes of a minimization problem since the critical exponent appears and the lower order term may change sign we should use more delicate arguments

diffusion in a one dimensional random medium and hyperbolic brownian motion classical diffusion in a random medium involves an exponential functional of brownian motion this functional also appears in the study of brownian diffusion on a riemann surface of constant negative curvature we analyse in detail this relationship and study various distributions using stochastic calculus and functional integration

quasilinear schrodinger equations with nonlinearities interacting with high eigenvalues it is the established existence and multiplicity of solutions for quasilinear schrodinger equations where the nonlinear term is 3 superlinear or 3 asymptotically linear at infinity in an appropriate sense the main difficulty arises from the fact that the nonlinearity has an interaction with high eigenvalues for the linear eigenvalue problem under these conditions we consider a local linking theorem together with a compactness result in order to ensure our main results we consider two distinct eigenvalues problems and some kind of crossing of eigenvalues it is the established existence and multiplicity of solutions for quasilinear schrodinger equations where the nonlinear term is 3 superlinear or 3 asymptotically linear at infinity in an appropriate sense the main difficulty arises from the fact that the nonlinearity has an interaction with high eigenvalues for the linear eigenvalue problem under these conditions we consider a local linking theorem together with a compactness result in order to ensure our main results we consider two distinct eigenvalues problems and some kind of crossing of eigenvalues

multiple solutions for quasilinear schrodinger equations with a parameter abstract in this paper we study the following quasilinear schrodinger equations of the form u v x u u 2 u 2 2 u g x u x r n where 1 1 2 v c r n r g c r n r r using some special techniques the existence of positive solutions negative solutions and sequence of high energy solutions are studied

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

information gain within nonextensive thermostatistics we discuss the information theoretical foundations of the kullback information gain recently generalized within a nonextensive thermostatistical formalism general properties are studied and in particular a consistent test for measuring the degree of correlation between random variables is proposed in addition minimum entropy distributions are discussed and the h theorem is proved within the generalized context

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

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

infinitely many solutions of quasilinear schrodinger equation with sign changing potential abstract in this paper we study the following quasilinear schrodinger equation of the form u v x u u 2 u g x u x r n where the potential v x is allowed to be sign changing and the primitive of the nonlinearity g x u is of superlinear growth at infinity in u and is also allowed to be sign changing we obtain the existence of infinitely many nontrivial solutions by using dual approach and mountain pass theorem

standing waves for quasilinear schrodinger equations with indefinite potentials abstract we consider quasilinear schrodinger equations in r n of the form u v x u u u 2 g u where g u is 4 superlinear unlike all known results in the literature the schrodinger operator v is allowed to be indefinite hence the variational functional does not satisfy the mountain pass geometry by a local linking argument and morse theory we obtain a nontrivial solution for the problem in case that g is odd we get an unbounded sequence of solutions

existence and multiplicity results for periodic solutions of semilinear duffing equations we obtain existence an multiplicity of harmonic and subharmonic solutions to the periodically forced nonlinear duffing s equation x g x p t in the semi linear case 0 a g x x b for x large we introduce new conditions of nonresonance with respect to the spectrum of the associated linear differential operator x x and show by some nonlinear counterexamples that the results are sharp

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 solution for a generalized quasilinear elliptic problem it establishes existence and multiplicity of solutions to the elliptic quasilinear schrodinger equation div g2 u u g u g u u 2 v x u h x u x n where g h v are suitable smooth functions the function g is asymptotically linear at infinity and for each fixed x n the function h x s behaves like s at the origin and s3 at infinity in the proofs we apply variational methods

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