on the palais smale condition abstract we present a new sufficient assumption weaker than the classical ambrosetti rabinowitz condition which guarantees the boundedness of ps sequences moreover we relax the standard subcritical polynomial growth condition ensuring the compactness of a bounded ps sequences we also revise the costa magalhaes condition 8 to obtain cerami condition as a consequence some existence results derived by minimax methods were proved finally we establish the existence of positive solution under the subcritical polynomial growth condition while the strong superlinear condition is only required along an unbounded sequence in other words a certain degraded oscillation is allowed

existence and non existence of nontrivial solutions for schrodinger systems via nehari pohozaev manifold abstract this paper is concerned with existence of bound states for a coupled gradient system of nonautonomous schrodinger equations which arises from studies of nonlinear optics and bose einstein condensates by using variational methods that are constrained to a nehari pohozaev manifold we obtain existence of nonnegative and positive bound states solutions in particular we show non existence result for a minimizing problem

multiple solutions for asymptotically linear elliptic systems in this article we consider cooperative and noncooperative elliptic systems that are asymptotically linear at infinity we obtain infinitely many solutions with small energy if the potential is even if the noncooperative system is resonant both at zero and at infinity then the number of nontrivial solutions depends on the dimension of the eigenspaces between resonant values

asymptotically linear cooperative elliptic system existence and multiplicity abstract in this paper we consider an asymptotically linear cooperative elliptic system at resonance by a penalization technique and by the use of morse theory we prove firstly the existence of a non zero solution if the difference between the morse index at zero and the morse index at infinity is big enough later on we will prove the existence of n 1 pairs of non trivial solutions where n is roughly speaking the difference between the morse index at zero and the morse index at infinity

free vibrations for a semilinear wave equation abstract existence and regularity of nontrivial time periodic solutions are proved for semilinear wave equations under mild smoothness monotonicity and superlinearity assumptions the forced vibration case is also treated

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

the existence of asymptotically unbiased nonnegative quadratic estimates of variance components in anova models abstract conditions for the existence of asymptotically unbiased nonnegative quadratic estimates of individual variance components in general anova models are investigated a simple necessary condition for general models is obtained necessary and sufficient conditions are obtained in the case of random balanced nested classification models and the random unbalanced one way model the investigation demonstrates the need for exercising caution when employing nonnegative quadratic estimates of individual variance components in practice

on ground states of superlinear p laplacian equations in rn abstract we consider superlinear p laplacian equations in r n with a potential which is periodic or has a bounded potential well without assuming the ambrosetti rabinowitz type condition and the monotonicity of the function t f x t t p 1 we prove the existence of ground states even for the case p 2 our results extend the recent results of li wang and zeng ann inst h poincare anal non lineaire 23 2006 829 837

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

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

existence results for the positive solutions of nonlinear elliptic systems in this paper we discuss the existence of solutions for nonlinear elliptic systems the positive weak solution is sought by the leray schauder degree

existence and multiplicity of solutions for asymptotically linear noncooperative elliptic systems abstract using the minimax methods in critical point theory and a generalized landesman lazer type condition we establish two existence results of solutions for asymptotically linear noncooperative elliptic systems at resonance besides this we obtain two solutions in the case of near resonance

periodic and subharmonic solutions for a class of superquadratic hamiltonian systems abstract some existence theorems are obtained for periodic and subharmonic solutions of a class of superquadratic hamiltonian systems by the minimax methods in critical point theory specially a local link theorem due to li and willem and the generalized mountain pass theorem respectively

morse homology of super quadratic hamiltonian systems on r2n abstract we study periodic solutions of the hamiltonian system x t j h t x where j is the standard symplectic matrix h is 2 periodic in t and super quadratic in x in some sense using the morse homology theory developed in a abbondandolo p majer morse homology on hilbert spaces comm pure appl math 54 2001 689 758 we get some existence results of periodic solutions

an existence result for gradient type systems with a nondifferentiable term on unbounded strips in this paper we study the existence of nontrivial solutions for a class of gradient type systems on strip like domains where the nonlinear term is not necessarily continuously differentiable the proof of the main result is based on a nonsmooth version of the mountain pass theorem which involves the cerami compactness condition and on the principle of symmetric criticality for locally lipschitz functions

multiple critical points of invariant functionals and applications abstract this paper deals with some multiplicity results of periodic orbits of hamiltonian systems and for solution of a non linear dirichlet problem these results follow from an abstract theorem of lusternik schnirelman type as applied to an invariant equation of the form lu delta f u 0 in a hilbert space x l sub 2 omega r sub n where l is an unbounded self adjoint operator and f is a c sub 1 strictly convex function author

existence of solutions for perturbed fractional p laplacian equations abstract the purpose of this paper is to investigate the existence of weak solutions for a perturbed nonlinear elliptic equation driven by the fractional p laplacian operator as follows p s u v x u p 2 u a x u r 2 u b x u q 2 u in r n where is a real parameter p s is the fractional p laplacian operator with 0 s 1 p p r min q p s and v a b r n 0 are three positive weights using variational methods we obtain nonexistence and multiplicity results for the above mentioned equations depending on and according to the integrability properties of the ratio a q p b r p our results extend the previous work of autuori and pucci 2013 5 to the fractional p laplacian setting furthermore we weaken one of the conditions used in their paper hence the results of this paper are new even in the fractional laplacian case

a local min max orthogonal method for finding multiple solutions to noncooperative elliptic systems a local min max orthogonal method together with its mathematical justification is developed in this paper to solve noncooperative elliptic systems for multiple solutions in an order first it is discovered that a noncooperative system has the nature of a zero sum game a new local characterization for multiple unstable solutions is then established under which a stable method for multiple solutions is developed numerical experiments for two types of noncooperative systems are carried out to illustrate the new characterization and method several important properties for the method are explored or verified multiple numerical solutions are found and presented with their profiles and contour plots as a new bifurcation phenomenon multiple asymmetric positive solutions to the second type of noncooperative systems are discovered numerically but are still open for mathematical verification

the existence of solutions for a class of semilinear elliptic systems in this paper some new existence theorems of weak solutions for a class of semilinear elliptic systems are obtained by means of the local linking theorem and the saddle point theorem

viscosity solutions of fully nonlinear parabolic systems abstract in this paper we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second order degenerate parabolic equations and their cauchy dirichlet problem we prove the existence uniqueness and continuity of viscosity solution by combining perron s method with the technique of coupled solutions the results here generalize those in proc london math soc 63 1991 212 240 and comm partial differential equations 16 1991 1095 1128

on tests of the overall treatment effect in meta analysis with normally distributed responses for the meta analysis of controlled clinical trials or epidemiological studies in which the responses are at least approximately normally distributed a refined test for the hypothesis of no overall treatment effect is proposed the test statistic is based on a direct estimation function for the variance of the overall treatment effect estimator as outcome measures the absolute and the standardized difference between means are considered in simulation studies it is shown that the proposed test keeps the prescribed significance level very well in contrast to the commonly used tests in the fixed effects and random effects model respectively which can become very liberal furthermore just for using the proposed test it is not necessary to choose between the fixed effects and the random effects approach in advance

asymptotically linear schrodinger equations with sign changing potential abstract in this paper we show that the following system 0 1 u v x u g x v v v x v f x u x r n possesses at least one non trivial solution pair u v where f x t g x t are continuous functions on r n r and asymptotically linear as t and v x is allowed to be sign changing

on superquadratic elliptic systems in this article we study the existence of solutions for the elliptic system updelta u frac partial h partial v left u v x right text in upomega updelta v frac partial h partial v left u v x right text in upomega u 0 v 0 text on partial upomega where upomega is a bounded open subset of mathbb r n with smooth boundary partial upomega and the function h mathbb r 2 times overline upomega to mathbb r is of class c 1

existence of solutions for a dirichlet problem with a p laplacian abstract some theorems of existence of weak solutions are obtained for p laplacian equations with dirichlet boundary conditions by using a critical point theorem

multiple solutions for resonant elliptic equations via local linking theory and morse theory abstract we consider two classes of elliptic resonant problems first by local linking theory we study the double double resonant case and obtain three solutions second we introduce some new conditions and compute the critical groups both at zero and at infinity precisely combining morse theory we get three solutions for the completely resonant case

multiplicity and concentration of solutions for elliptic systems with vanishing potentials abstract in this article we use variational methods to study a strongly coupled elliptic system depending on a positive parameter we suppose that the potentials are nonnegative and the intersection of the sets where they vanish has positive measure a technical condition imposed on the product of the potentials allows us to consider a setting where we do not assume any positive lower bound for the potentials considering the associated functional defined on an appropriated subspace of d 1 2 r n d 1 2 r n we are able to establish results on the existence and multiplicity of solutions for the system when the parameter is sufficiently large we also study the asymptotic behavior of these solutions when

multiplicity of solutions for resonant elliptic systems we establish the existence and multiplicity of solutions for some resonant elliptic systems the results are proved by applying minimax arguments and morse theory

remarks on multiple nontrivial solutions for quasi linear resonant problems in this paper morse theory and local linking are used to study the existence of multiple nontrivial solutions for a class of dirichlet boundary value problems with double resonance at infinity and at 0

variance component estimation with model based diagnostics the problem of estimating variance components in mixed linear models has no satisfactory solution for the unbalanced data case further there has been little work on diagnostic methods for assessing the data and the model in this article we propose a new class of unbiased estimators these estimators have simple closed form expressions allowing for smallsample analysis and easy computations the structure of the estimators reveals natural diagnostics for examining the data and the model assumptions the source of negative estimates of variance components is revealed limited efficiency studies indicate that these estimators are comparable to existing estimators the estimators are illustrated by two numerical examples that reveal the importance of the diagnostic analysis

existence and multiplicity of solutions for a class of elliptic boundary value problems abstract in this paper we investigate the existence and multiplicity of solutions for the following elliptic boundary value problems u a x u g x u in u 0 on where g x u k u x u w u x u by using the symmetric mountain pass theorem we obtain two results about infinitely many solutions when g x u is odd in u k satisfies the pinching condition and w has a super quadratic growth moreover when the condition g x u is odd is not assumed by using the mountain pass theorem we also obtain two existence results of one nontrivial weak solution one of these results generalizes a recent result in mao zhu and luan 2012 10

global bifurcations of critical orbits of g invariant strongly indefinite functionals abstract let h be a separable hilbert space which is an orthogonal representation of a compact lie group g and let h r be a g invariant strongly indefinite functional of the class c 1 to study critical orbits of we have defined the degree for g invariant strongly indefinite functionals which is an element of the euler ring u g using this degree we have formulated the rabinowitz alternative for g invariant strongly indefinite functionals the abstract results are applied to the study of global bifurcations of weak solutions of non cooperative systems of elliptic differential equations

existence results for some nonlinear elliptic systems abstract the paper is concerned with some nonlinear elliptic systems by using variational methods we obtain the existence of weak solutions for the semilinear elliptic system and the quasilinear elliptic system

jordan algebras and bayesian quadratic estimation of variance components the authors consider a linear model ey x cov y v where v is a quadratic subspace a jordan algebra using this property it is shown how multiplication computation of g inverses determination of a neutral element can be done more efficiently in v finally this technique is applied to obtain formulae for locally optimal estimators and bayesian estimators

on a class of asymptotically linear elliptic problems in rn under these conditions p is an asymptotically linear problem when this equation is considered in a bounded domain 0 r with say the dirichlet boundary condition there is a large literature on existence and multiplicity results of particular interest is then the case of resonance where s and s is the asymptotic linearization of the problem in other words s d s l 0 l 0 is the operator given by

a variational approach to subquadratic perturbations of elliptic systems abstract we consider subquadratic perturbations of semilinear elliptic systems which are in variational form a unified approach to both the cooperative and noncooperative problems is presented and a condition of nonquadraticity at infinity is introduced to treat the resonant cases through minimax techniques

variational elliptic problems which are nonquadratic at infinity p co if n 1 2 then it is well known that the weak solutions u e h 2 of p are the critical points of the c functional j u ulvul dx jcf x u dx where f x s jif x t dt in this variational setting the literature usually distinguishes between two situations for prob lem p the subquadratic situation where the potential f satisfies lim suplsl f x s s2 i c m and the superquadratic situation where f satisfies limlsl m f x s s2 00 the main goal of this paper is to present a unified approach to both situations by means of a condition of nonquadraticity at infinity on f more precisely our hypotheses are as follows

quasilinear elliptic system with coupling on nonhomogeneous critical term abstract we study the existence of multiple solutions for a quasilinear elliptic system of gradient type with the possibility of coupling on the critical and subcritical terms which are not necessarily homogeneous the solutions are obtained from a version of the symmetric mountain pass theorem a version of the concentration compactness principle for this class of systems allows us to verify that the palais smale condition is satisfied below a certain level

a critical kirchhoff type problem involving a nonlocal operator abstract in this paper we show the existence of non negative solutions for a kirchhoff type problem driven by a nonlocal integrodifferential operator that is m u z 2 l k u f x u u 2 2 u in u 0 in r n where l k is an integrodifferential operator with kernel k is a bounded subset of r n m and f are continuous functions z is a functional norm and 2 is a fractional sobolev exponent

on the existence of unbiased nonnegative estimates of variance convariance components the existence of unbiased nonnegative definite quadratic estimates for linear combinations of variance covariance components is characterized by means of the natural parameter set in a residual model in the presence of a quadratic subspace condition the following disjunction for nonnegative estimability is derived either standard methods suffice or the concepts of unbiasedness and nonnegative definiteness are incompatible for the case of a single variance component it is shown that unbiasedness and nonnegative definiteness always entail a reduction to a trivial model in which the variance component under investigation is the sole remaining parameter several examples illustrate these results

an asymptotically linear non cooperative elliptic system with lack of compactness in this paper we consider an asymptotically linear non cooperative elliptic system at resonance the functional associated to the system is strongly indefinite and so the morse index of each critical point is infinite to overcome this difficulty we will use morse theory for strongly indefinite functionals developed by abbondandolo we shall prove that if the system has a non resonant solution the morse index of which is different from the morse index at infinity then there exists another solution

strongly indefinite functionals and multiple solutions of elliptic systems we study existence and multiplicity of solutions of the elliptic system left begin array 20 l updelta u h u x u v hfill text in upomega hfill updelta v h v x u v hfill text in upomega quad u x v x 0 quad text on partial upomega hfill end array right where upomega subset mathbb r n n ge 3 is a smooth bounded domain and h in mathcal c 1 overline upomega times mathbb r 2 mathbb r we assume that the nonlinear term h x u v sim left u right p left v right q r x u v text with mathop lim limits left u v right to infty frac r x u v left u right p left v right q 0 where p in 1 2 2 2n n 2 text and q in 1 infty so some supercritical systems are included nontrivial solutions are obtained when h x u v is even in u v we show that the system possesses a sequence of solutions associated with a sequence of positive energies resp negative energies going toward infinity resp zero if p 2 resp p 2 all results are proved using variational methods some new critical point theorems for strongly indefinite functionals are proved