on the existence of weak solutions of perturbated systems with critical growth sur un domaine borne de r n on considere le probleme de dirichlet pour le systeme elliptique a u g u f sur et u 0 ou a u est un operateur quasi lineaire et la perturbation g u depend de u et de d u on etudie des conditions suffisantes sur a u et sur g u pour l existence de solutions faibles

regularizing effect of absorption terms in singular problems abstract we prove existence of solutions to problems whose model is p u u q f u in u 0 in u 0 on where is an open bounded subset of r n n 2 p u is the p laplacian operator for 1 p n q 0 0 and f is a nonnegative function in l m for some m 1 in particular we analyze the regularizing effect produced by the absorption term in order to infer the existence of finite energy solutions in case 1 we also study uniqueness of these solutions as well as examples which show the optimality of the results finally we find local w 1 p solutions in case 1

local superlinearity and sublinearity for the p laplacian we study the existence nonexistence and multiplicity of positive solutions for a family of problems updelta p u f lambda x u u in w 0 1 p upomega where is a bounded domain in mathbb r n n p and 0 is a parameter the family we consider includes the well known nonlinearities of ambrosetti brezis cerami type in a more general form namely lambda a x u q b x u r where 0 leqslant q p 1 r leqslant p 1 here the coefficient a x is assumed to be nonnegative but b x is allowed to change sign even in the critical case preliminary results of independent interest include the extension to the p laplacian context of the brezis nirenberg result on local minimization in w 0 1 p text and c 0 1 a c 1 alpha estimate for equations of the form updelta p u h x u with h of critical growth a strong comparison result for the p laplacian and a variational approach to the method of upper lower solutions for the p laplacian

quasilinear elliptic problems with singular and homogeneous lower order terms abstract we deal with singular quasilinear elliptic equations namely u u x u q u q 1 f x in u 0 in u 0 on where is a bounded smooth domain of r n n 3 r 1 q 2 0 l and 0 f l p for some p n 2 we completely describe the set of values of the parameter for which the problem admits solution thus we study existence nonexistence and uniqueness of bounded weak solutions in both cases f 0 and f 0

existence of renormalized solutions to nonlinear elliptic equations with two lower order terms and measure data in this paper we prove the existence of a renormalized solution to a class of nonlinear elliptic problems whose prototype is formula maths where is a bounded open subset of r n n 2 ap is the so called p laplace operator 1 p n is a radon measure with bounded variation on 0 p 1 0 p 1 and c and b belong to the lorentz spaces l p 1 r n p 1 r and l n 1 respectively in particular we prove the existence under the assumptions that p 1 c belongs to the lorentz space ln p 1 r n p 1 r and c n r is small enough

on a singular elliptic system with quadratic growth in the gradient abstract in this paper we deal with the following singular elliptic system u u 2 u p p q a x v q u p 2 u f x r n v v 2 v q p q a x u p v q 2 v g x r n where n 3 n 2 4 p q 1 and p q n 2 n 2 we show through the sub and supersolutions method the existence of a nonnegative solution for an approximated system the limit of the approximated solution is a positive solution in the case 0 p q and f g we prove the uniqueness of a solution among others we prove some existence and uniqueness results for some auxiliary problems by using the comparison principle a minimization method and with the help of nehari manifold the proofs rely on the concentration compactness principle

the winding angle distribution of an ordinary random walk the winding angle about a selected point of a random walk quantifies what is perhaps the simplest manifestation of entanglement a phenomenon of great importance in the study of polymers the distribution of winding angles is studied here for ordinary or non self avoiding walks new results highlight the crucial influence of the exclusion of a finite region about the selected point on the winding angle distribution the results of this analysis are compared with simulations of random walks on a lattice the agreement between the two is very good there are however small and as yet unexplained discrepancies

existence and nonexistence of nontrivial solutions of some nonlinear degenerate elliptic equations in connection with the maximizing problem for the functional r u u lq u lp in w01 p 0 we consider the equation div u p 2 u x u q 2 u x x 1 p resp q p e has no nontrivial resp nonnegative nontrivial solution belonging to the class p u w01 p lq xi u q 2u lp p 1 i 1 2 n w01 p provided that is star shaped the crucial point of the proof of our result is to obtain an l estimate of weak solutions and to verify a certain pohozaev type inequality for weak solutions belonging to p

non linear elliptic and parabolic equations involving measure data in this paper we prove the existence of solutions for equations of the type div a du f in a bounded open set u 0 on where a is a possibly non linear function satisfying some coerciveness and monotonicity assumptions and f is a bounded measure we also consider the equation div a du g u f in u 0 on with f l1 or f m u u 0 and the parabolic equivalent of the first elliptic equation

solvability of perturbed elliptic equations with critical growth exponent for the gradient sur un domaine borne cr n on considere le probleme de dirichlet a u g u f u 0 ou a u t 1 n 1 d i a i x u d u definit un operateur pseudomonotone d un espace de sobolev h 0 1 p dans son espace dual et la perturbation g u g x u d u satisfait une condition de croissance

existence results for some quasilinear parabolic equations on considere le probleme de cauchy pour une equation dont la partie principale est un operateur parabolique quasilineaire le terme non lineaire additionnel a au plus une croissance quadratique par rapport au gradient de la solution on demontre l existence d une solution bornee faible sous des hypotheses de regularite minimales en supposant l existence d une sous solution et d une supersolution pour le probleme

the nehari manifold for systems of nonlinear elliptic equations abstract this paper deals with the existence and multiplicity results of nonlocal positive solutions to the following system p u u p 1 2 u 1 u u 1 v 1 q v v q 2 v 1 u 1 v 1 v together with dirichlet or mixed boundary conditions under some hypotheses on the parameters p p 1 and q more precisely the system considered corresponds to a perturbed eigenvalue equation combined with a second equation having concave and convex nonlinearities the study is based on the extraction of palais smale sequences in the nehari manifold the behaviour of the energy corresponding to these positive solutions with respect to the real parameters and is established

holder continuity of the inverse ofp laplacian abstract in this note we study the inverse operator p 1ofp lapalcian on a bounded domain rn we show that p 1 w 1 p w1 p0 is holder continuous and is a compact operator fromv q s tow1 p0 s 0 p q p the conjugate of critical sobolev exponent as an application we study existence of positive solutions of two nonlinear elliptic equations

lower semicontinuity of functionals via the concentration compactness principle in this paper we show the weak lower semicontinuity of some classes of functionals using the concentration compactness principle of p l lions these functionals involve an integral term and we do not know whether it can be handled by the de giorgi theorem the semicontinuity result allows us to prove several existence results for quasilinear elliptic equations

minimization problem associated with an improved hardy sobolev type inequality abstract we consider the existence or non existence of a minimizer of the following minimization problems associated with an improved hardy sobolev type inequality introduced by ioku 2019 i a inf u w 0 1 p b r 0 b r u p d x b r u p s v a x d x p p s where v a x 1 x s 1 a x r n p p 1 1 x s where 1 p n and 0 s p the minimization problem i a is equivalent to the minimization problem associated with the classical hardy sobolev inequality on r n via a transformation if we restrict ourselves to radial functions in contrast to the classical results for a 0 we show the existence of non radial minimizers for the hardy sobolev critical exponent p s p n s n p on bounded domains furthermore as an application of the transformation we derive an infinite dimensional form of the classical sobolev inequality in some sense

the nehari manifold for a semilinear elliptic system involving sign changing weight functions abstract in this paper we study the combined effect of concave and convex nonlinearities on the number of solutions for a semilinear elliptic system e with sign changing weight function with the help of the nehari manifold we prove that the system has at least two nontrivial nonnegative solutions when the pair of the parameters belongs to a certain subset of r 2

variations on a strange semi continuity result abstract this paper is devoted to the study of some lower semi continuity results whose model example is lim inf n u n v n u v for any sequence u n v n which weakly converges to u v in h 0 1 2 and satisfies the positivity assumptions u n 0 and v n 0 extensions of this semi continuity result are obtained in the following cases two fixed linear operators two monotone operators two varying linear operators varying domains and non uniformly bounded operators in these various cases the operators under consideration are second order elliptic operators in divergence form and truncation arguments play an essential role finally the case of higher order operators is treated by a quite different approach

characteristic function and spitzer s law for the winding angle distribution of planar brownian curves using the analogy between brownian motion and quantum mechanics the author studies the winding angle theta of planar brownian curves around a given point say the origin o in particular the author computes the characteristic function for the probability distribution of theta and recovers spitzer s law in the limit of infinitely large times

a new approach for numerical modal analysis using the element free method a novel approach in analysing the vibration of elastic body systems is presented and discussed in this paper this method uses a meshless spatial approximation based only on nodes which constitutes an advantage over the finite element method as it is applicable to an elastic body with arbitrary shape it also has advantages over the classical rayleigh ritz method and its extensions the paper is organized as follows in section 2 hamilton s principle is used for obtaining the equations of motion for a three dimensonal simply connected elastic body in section 3 the development of weighted base functions for the moving least squares interpolant is described in section 4 the mass and stiffness matrices are derived using the previous results in section 5 a system synthesis description is given in which we also develop the approach used for integrating the boundary conditions finally in section 6 the theoretical results are validated by case studies chosen to highlight various features of the approach including optimization of the shape function parameters the particle method has already been used for structural dynamics liu et al international journal for numerical methods in engineering 1995 38 1655 1679 but for free vibration of beams and plates to the authors knowledge this paper is the first application of the element free method to modal analysis copyright c 1999 john wiley sons ltd

mountain pass solutions for quasi linear equations via a monotonicity trick abstract we obtain the existence of symmetric mountain pass solutions for quasi linear equations without the typical assumptions which guarantee the boundedness of an arbitrary palais smale sequence this is done through a recent version of the monotonicity trick proved in squassina in press 22 the main results are new also for the p laplacian operator

existence and non existence of positive solutions for nonlinear elliptic singular equations with natural growth abstract in this paper we analyze the existence non existence and uniqueness of positive solutions of some nonlinear elliptic equations containing singular terms and natural growth in the gradient term we use an adequate sub super solution method to prove the existence of solutions the characterization of eigenvalues and the integrability of the term u 2 u 2 for the non existence and results from arcoya segura de leon for the uniqueness

existence result for quasilinear elliptic problem on unbounded domains abstract in this paper we obtain the existence of a nontrivial solution for inhomogeneous quasilinear elliptic systems on arbitrary domains with lack of compactness the method used here is essentially based on preliminary results on the convergence almost everywhere of the gradients of palais smale sequences

regularizing effect for some p laplacian systems abstract we study existence and regularity of weak solutions for the following p laplacian system p u a 1 u r 2 u f u w 0 1 p p u r w 0 1 p where is an open bounded subset of r n n 2 p v div v p 2 v is the p laplacian operator for 1 p n a 0 r 1 0 p 1 and f belongs to a suitable lebesgue space in particular we show how the coupling between the equations in the system gives rise to a regularizing effect producing the existence of finite energy solutions

asymptotic behaviour of linear dirichlet parabolic problems with variable operators depending on time in varying domains abstract we study the asymptotic behaviour of the solutions of linear parabolic dirichlet problems when the coefficients and the domains where the problems are posed vary simultaneously in the limit problem it appear the h limit of the operators and as it is usual in the homogenization of dirichlet problems a new term of order zero we also obtain a corrector result

shape optimisation problems governed by nonlinear state equations the purpose of this paper is to give a compactness continuity result for the solution of a nonlinear dirichlet problem in terms of its domain variation the topology in the family of domains is given by the hausdorff metric and continuity is obtained under capacity conditions a generalisation of sverak s result in iv dimensions is deduced as a particular case

existence of entire positive solutions for a critical system of nonlinear elliptic equations abstract in this paper using the fibering method introduced by pohozaev we establish an existence of multiple nontrivial positive solutions for a system of nonlinear elliptic equations in r n with lack of compactness studying the properties of palais smale sequence of the energy functional associated with the system

magnetic fields and brownian motion on the 2 sphere using constrained path integrals the authors study some statistical properties of brownian paths on the two dimensional sphere a generalized levy law for the probability p a that a closed brownian path encloses an algebraic area a is obtained distributions of scaled variables related to the winding of paths around some fixed point are recovered in the asymptotic regime t to infinity

strongly nonlinear parabolic equations with natural growth terms in orlicz spaces abstract we prove approximation and compactness results in inhomogeneous orlicz sobolev spaces and look at as an application the cauchy dirichlet equation u a u g x t u u f w 1 x e m where a is a leray lions operator having a growth not necessarily of polynomial type we also give a trace result allowing to deduce the continuity of the solutions with respect to time

ground states of degenerate quasilinear schrodinger equation with vanishing potentials abstract in this paper we study the existence of nontrivial ground state solutions for the following class of p laplacian type equation div a x u v x x p u p 2 u k x x p f u in r n where 1 p n n 3 n p p e 1 d 1 e p p e n p n d p critical hardy sobolev exponent f has a quasicritical growth v and k are nonnegative potentials the function a satisfies a x u c 0 x p h 0 x u p 1 c 0 1 x p h 1 x u p 1 for any r n a e x r n for any two positive functions h 1 l l o c r n h 0 l p p 1 r n with p p

the extinction versus the blow up global and non global existence of solutions of source types of degenerate parabolic equations with a singular absorption abstract we consider nonnegative solutions of degenerate parabolic equations with a singular absorption term and a source nonlinear term t u u x p 2 u x x u u 0 f u x t in i 0 t with the homogeneous zero boundary condition on i x 1 x 2 an open bounded interval in r through this paper we assume that p 2 and 0 1 to show the local existence result we prove first a sharp pointwise estimate for u x one of our main goals is to analyze conditions on which local solutions can be extended to the whole time interval t 0 the so called global solutions or by the contrary a finite time blow up 0 0 arises such that lim t 0 u t l i moreover we prove that any global solution must vanish identically after a finite time if provided that either the initial data or the source term is small enough finally we show that the condition f 0 x t 0 x t i 0 is a necessary and sufficient condition for the existence of solution of equations of this type

an existence result for a class of pp laplacian elliptic systems involving homogeneous nonlinearities in rn abstract in the present paper we study the existence of nontrivial solutions for a class of p laplacian elliptic systems in r n a new existence result for nontrivial solutions is obtained by means of variational methods

anisotropic elliptic equations with general growth in the gradient and hardy type potentials abstract in this paper we give existence and regularity results for the solutions of problems whose prototype is q v v h d v q h o x p v p 2 v f x in v 0 on with bounded domain of r n n 2 0 p 1 q p n is a nonnegative continuous function and 0 moreover h is a general norm of r n h o is its polar and q v i 1 n x i h d v p 1 h i d v

multiplicity result for some nonlocal anisotropic equation via nonsmooth critical point theory approach abstract in this paper we study quasilinear problems involving variable exponent growth conditions and nonlocal terms on the whole space r n a multiplicity result is established all the coefficients involved in the terms of the equation depend both on the variable x and the unknown function u our main argument is nonsmooth critical point theory

existence results for some nonlinear elliptic system with lack of compactness abstract we are interested in existence of solutions for some typical elliptic systems governed by two pseudo laplacian operators with critical sobolev exponents we show this result by a local minimization for an adapted variational problem a concentration compactness principle allows us to obtain some convergence results

the nehari manifold for indefinite semilinear elliptic systems involving critical exponent abstract in this paper we study the combined effect of concave and convex nonlinearities on the number of solutions for an indefinite semilinear elliptic system e involving critical exponents and sign changing weight functions using nehari manifold the system is proved to have at least two nontrivial nonnegative solutions when the pair of the parameters belongs to a certain subset of r 2

a fully symbolic generation of the equations of motion of multibody systems containing flexible beams the modelling of flexible elements in mechanical systems has been investigated via several methods issuing from both the field of multibody dynamics and the area of structural mechanics and vibration theory a multibody approach using a recursive formalism in relative coordinates is adopted here while leading to a highly non linear system with a dense mass matrix relative coordinates allow the setting up of the minimal set of equations of motion for open loop systems as for the recursive technique the latter was proved to be a very good candidate for an optimized symbolic generation in the case of rigid multibody systems these two assertions have led us to generalize such a formalism for a general multibody system containing flexible beams in order to make its fully symbolic generation possible within the stand alone program robotran 1 several validation examples are presented to illustrate the method and to highlight the efficiency and the user friendliness of this fully symbolic model even when dealing with beams undergoing large motions

a quasilinear dirichlet problem with quadratic growth respect to the gradient and l1 data abstract for an open bounded set r n measurable bounded functions a x b x which are strictly positive and p q 0 we prove the existence of a weak solution of the quasilinear b v p div a x u q u x b x u u p 1 u 2 f x x u x 0 x the datum f is assumed to be in l 1 and does not satisfy any sign assumption

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

existence and nonexistence of solutions for singular quadratic quasilinear equations we study both existence and nonexistence of nonnegative solutions for nonlinear elliptic problems with singular lower order terms that have natural growth with respect to the gradient whose model is 8

nontrivial solutions for perturbations of a hardy sobolev operator on unbounded domains in this paper we study the existence of nontrivial solution of the problem pu d x p u p 2u f u in and u 0 on where rn k is a bounded domain with smooth boundary in rk 1 k n existence is established using mountain pass lemma and concentration of compactness principle

a robin problem for a class of quasilinear operators and a related minimizing problem abstract in this paper we establish the existence of multiple radial solutions for a class of quasilinear operators with nonlinear boundary robin conditions besides other conditions we consider the nonlinearities having a behavior at at least like a linearity of slope less than first eigenvalue 1 r the technical approach is by variational methods which is mainly based on a version of mountain pass theorem due to ghoussoub and preiss

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

multiple positive solutions for a quasilinear elliptic equation with critical exponential nonlinearity abstract let be a bounded domain in r n n 2 with c 2 boundary in this work we study the existence of multiple positive solutions of the following problem p div u 2 n 2 1 u 2 n u u 2 n 2 1 u 2 n u u p e u n n 1 u 0 in u 2 n 2 1 u 2 n u u q on where 0 p 2 n 1 q 0 n 1 and is a non negative holder continuous function we show that there exists 0 such that p admits at least two solutions in w 1 n for 0 and no solution for

multiplicity results for problems involving the hardy sobolev operator via morse theory we establish some multiplicity results for a class of boundary value problems involving the hardy sobolev operator using morse theory c 2009 elsevier ltd all rights reserved

an efficient general approach to modal analysis of frame resonators with applications to support loss in microelectromechanical systems abstract the design of high q resonators such as xylophone bar resonators xbrs capable of being fabricated using micro electro mechanical systems mems processes is of considerable interest in light of the widespread and rapidly growing use of systems dependent on their availability and performance this paper is concerned with vibration analysis and q optimisation of an xbr with the method extending directly to other planar frames and straightforwardly to more complex structures the rayleigh ritz method is discussed in some detail first treating the discrete case followed by developing and applying a kinematical procedure to an l frame structure attention is given to geometric interpretation of the rayleigh ritz procedure and to developing an intuitive understanding the method before turning to the xbr case having developed an approximation for system dynamics the results are used in conjunction with an analytical model of elastic wave propagation in the substrate to obtain an estimate for the support q factor natural frequencies mode shapes and support q values are presented and compared to finite element models of the same problem with excellent agreement observed at substantially lower computational cost for the first time in the literature the geometric impedance tuning principle underlying the xbr design is validated and quantified including sensitivity to manufacturing error

critical growth fractional elliptic systems with exponential nonlinearity abstract we study the existence of positive solutions for the system of fractional elliptic equations of the type 1 2 u p p q f x u p 2 u v q h 1 u v e u 2 v 2 in 1 1 1 2 v q p q f x u p v q 2 v h 2 u v e u 2 v 2 in 1 1 u v 0 in 1 1 u v 0 in r 1 1 where 1 p q 2 h 1 u v 2 u 2 u 2 u v h 2 u v 2 v 2 u v 2 v and 2 here 1 2 is the fractional laplacian operator we show the existence of multiple solutions for suitable range of by analyzing the fibering maps and the corresponding nehari manifold we also study the existence of positive solutions for a superlinear system with critical growth exponential nonlinearity

numerical modal analysis of structures based on a revised substructure synthesis approach the classical substructuring approach to the problem of modal analysis of structures suffers from a number of drawbacks which can sometimes lead the analyst to prefer other often more cumbersome techniques a modified rayleigh ritz based approach is presented which circumvents most of the drawbacks and improves the precision of the method while also enhancing its applicability to complex structures the scheme is also particularly well suited to symbolic implementation in view of its systematic problem independent formulation the theoretical results are validated by case studies chosen to highlight various features of the approach viz a beam structure a hinged simple square plate a hinged plate structure of fairly complicated shape and a rectangular plate with two cutouts

mountain pass solutions for the coupled systems of second and fourth order elliptic equations abstract in this paper by the mountain pass theorem we give an existence theorem of nontrivial solutions for a coupled system of second and fourth order elliptic equations

optimal results for parabolic problems arising in some physical models with critical growth in the gradient respect to a hardy potential abstract we deal with the following parabolic problem u t u u p u x 2 f u 0 in 0 t u x t 0 on 0 t u x 0 u 0 x x where r n n 3 is a bounded regular domain such that 0 or r n p 1 0 and f 0 u 0 0 are in a suitable class of functions there are deep differences with respect to the heat equation 0 the main features in the paper are the following if 0 there exists a critical exponent p such that for p p there is no nontrivial local solution p is optimal in the sense that if p p there exists solution for suitable data if we consider the cauchy problem i e r n we find the same phenomenon about the critical power p as above moreover there exists a fujita type exponent f p in the sense that independently of the initial datum for 1 p f any solution blows up in a finite time respect to an integral norm this is a major difference with respect to the heat equation 0

existence and asymptotic behavior of solutions for a class of neumann problems in this paper we study the existence of solutions u w1 p and their asymptotic behavior for the problem e2 pu f u in u 0on where p is the p laplace operator

a nonlinear parabolic problem with singular terms and nonregular data abstract we study existence of nonnegative solutions to a nonlinear parabolic boundary value problem with a general singular lower order term and a nonnegative measure as nonhomogeneous datum of the form u t p u h u f in 0 t u 0 on 0 t u u 0 in 0 where is an open bounded subset of r n n 2 u 0 is a nonnegative integrable function p is the p laplace operator is a nonnegative bounded radon measure on 0 t and f is a nonnegative function of l 1 0 t the term h is a positive continuous function possibly blowing up at the origin furthermore we show uniqueness of finite energy solutions in presence of a nonincreasing h

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

the p dirichlet to neumann operator with applications to elliptic and parabolic problems abstract in this paper we investigate the dirichlet to neumann operator associated with second order quasi linear operators of p laplace type for 1 p which acts on the boundary of a bounded lipschitz domain in r d for d 2 we establish well posedness and holder continuity with uniform estimates of weak solutions of some elliptic boundary value problems involving the dirichlet to neumann operator by employing these regularity results of weak solutions of elliptic problems we show that the semigroup generated by the negative dirichlet to neumann operator on l q enjoys an l q c 0 smoothing effect and the negative dirichlet to neumann operator on the set of continuous functions on the boundary of the domain generates a strongly continuous and order preserving semigroup moreover we establish convergence in large time with decay rates of all trajectories of the semigroup and in the singular case 1 e 2 d d 2 p 2 for some e 0 we give upper estimates of the finite time of extinction

a gradient estimate to a degenerate parabolic equation with a singular absorption term the global quenching phenomena we prove global existence of nonnegative solutions to the one dimensional degenerate parabolic problems containing a singular term we also show the global quenching phenomena for l1 initial datums moreover the free boundary problem is considered in this paper

multiple critical points for nondifferentiable functionals involving hardy potentials abstract in this paper we study general functionals of the calculus of variations with the presence of a hardy potential we will improve several results obtained in the semilinear framework we will first prove a general weak lower semicontinuity result which will imply the existence of a minimum point whenever the functional is coercive then we will demonstrate existence and multiplicity results of critical points even if our functional is not differentiable we will apply a nonsmooth critical point theory developed in corvellec et al nonlinear anal 1 1993 151 and degiovanni and marzocchi ann mat pura appl 167 1994 73

some elliptic problems with singular natural growth lower order terms abstract in this paper we deal with a nonlinear elliptic problem whose model is u b d u 2 u f in u 0 on where b 0 and f 0 belongs to a lebesgue space we prove the existence of positive solutions in suitable sobolev spaces depending on f and b

existence of a continuum of solutions for a quasilinear elliptic singular problem abstract in this paper we study the existence of positive solution u h 0 1 for some quasilinear elliptic equations having lower order terms with quadratic growth in the gradient and singularities whose model is u x u 2 u u u p f 0 x x 0 0 p using topological methods we obtain the existence of an unbounded continuum of solutions in the case x is constant we derive the existence of solution for every 0 if 1 2 for any and p 1 even more for l we prove this result if 1 and p 2

on a nonhomogeneous elliptic system with changing sign data abstract in this paper we give some existence results for multiple positive solutions to the following nonhomogeneous elliptic system s u a u 1 u u 1 v 1 f x in v b v 1 u 1 v v 1 g x in u v 0 on where is a regular bounded domain in r n n 3 0 a b nonnegative reals and are positive parameters and f g are given changing sign functions