existence and multiplicity of solutions for elliptic systems with nonstandard growth condition in rn abstract in this paper we study the elliptic system of gradient type with nonstandard growth conditions in r n existence and multiplicity results under two growth conditions on the reaction terms are established

existence of positive solutions for 2nth order singular sublinear boundary value problems abstract this paper investigates the existence of positive solutions for 2nth order n 1 singular sub linear boundary value problems a necessary and sufficient condition for the existence of c 2 n 2 0 1 as well as c 2 n 1 0 1 positive solutions is given by constructing lower and upper solutions and with the maximal theorem our nonlinearity f t x 1 x 2 x n may be singular at x i 0 i 1 2 n t 0 and or t 1

on fourth order elliptic boundary value problems with nonmonotone nonlinear function this paper is concerned with the fourth order elliptic boundary value problems with nonmonotone nonlinear function the existence and uniqueness of a solution is proven by the method of upper and lower solutions a monotone iteration is developed so that the iteration sequence converges monotonically to a maximal solution or a minimal solution depending on whether the initial iteration is an upper solution or a lower solution

qualitative properties and support compactness of solutions for quasilinear schrodinger equation with sign changing potentials abstract in this paper we deal with the following general elliptic equation involving the weigh p laplace operator p u v x u a x u q 1 u x r n where n 3 p 2 0 q and a x v x change sign in r n the main result of this work establishes some qualitative properties of the solutions of the above equation more precisely in a first part we study the compactness of support of classical solutions in the second part we study the behavior and the qualitative properties of the radial classical solutions and we give a classification of these solutions

multiple positive radial solutions for a dirichlet problem involving the mean curvature operator in minkowski space abstract we study the dirichlet problem with mean curvature operator in minkowski space div v 1 v 2 x v q 0 in b r v 0 on b r where 0 is a parameter q 1 r 0 0 r is continuous strictly positive on 0 and b r x r n x r using upper and lower solutions and leray schauder degree type arguments we prove that there exists 0 such that the problem has zero at least one or at least two positive radial solutions according to 0 or moreover is strictly decreasing with respect to r

stationary surfaces in lorentz minkowski space consider a spacelike plane in minkowski space under the presence of a uniform timelike potential directed towards this paper analyzes the conflgurations of shapes that shows a spacelike surface supported in with prescribed volume and that it is a critical point of the energy of this system such surface is called stationary and it is determined by the condition that the mean curvature is a linear function of the distance from and the fact that the angle of contact with the plate is constant we prove that the surface must be rotational symmetric with respect to an axis orthogonal to next we show existence and uniqueness of symmetric solutions for a prescribed angle of contact with finally we shall study the shapes that a stationary surface can adopt in terms of its size so we shall derive estimates of its height and the enclosed volume by surface with the support plane

positive solutions of the dirichlet problem for the prescribed mean curvature equation in minkowski space abstract we prove the existence of multiple positive solutions of the dirichlet problem for the prescribed mean curvature equation in minkowski space div u 1 u 2 f x u u in u 0 on here is a bounded regular domain in r n and the function f f x s is either sublinear or superlinear or sub superlinear near s 0 the proof combines topological and variational methods

uniqueness theorems for positive radial solutions of quasilinear elliptic equations in a ball we establish a new pohozaev type identity and use it to prove a theorem on the uniqueness of positive radial solutions to the quasilinear elliptic problem div u m 2emsp14 u f u 0 inb andu 0 on b wherebis a finite ball in rn n 3 and 1 0 and 1 p q n 2 n 2 has a unique positive solution whenn 6 this gives a complete answer to an open problem raised by brezis and nirenberg in 1983 in the casen 6 we shall also derive some partial results to the open problem in the casesn 3 4 5

entire solutions of quasilinear elliptic equations abstract we consider the existence of entire solutions of a quasilinear elliptic equation div d u p 2 d u k x f u x r n where p 1 n n conditions of the existence of entire solutions have been obtained by different authors we prove an optimality of some of these results and give new sufficient conditions for the nonexistence of entire solutions

quasilinear elliptic problems in r n involving oscillatory nonlinearities in this paper we study an elliptic problem in r n which involves the p laplacian p n 2 and the nonlinear term has an oscillatory behavior by means of a direct variational approach we establish the existence of infinitely many homoclinic solutions whose w 1 p r n norms tend to zero to infinity respectively whenever the nonlinearity oscillates at zero at infinity respectively the solutions have invariance properties with respect to certain subgroups of the orthogonal group o n

triple positive solutions and dependence on higher order derivatives abstract in this paper we consider the lidstone boundary value problem y 2 m t f y t y 2 j t y 2 m 1 t 0 t 1 y 2 i 0 0 y 2 i 1 0 i m 1 where 1 m f 0 growth conditions are imposed on f and inequalities involving an associated green s function are employed which enable us to apply the leggett williams fixed point theorem to cones in ordered banach spaces this in turn yields the existence of at least three positive symmetric concave solutions the emphasis here is that f depends on higher order derivatives

on positive radial entire solutions of second order quasilinear elliptic systems abstract we study positive radial entire solutions of second order quasilinear elliptic systems of the form p u f x u v q v g x u v x r n sufficient and or necessary conditions of f and g are obtained for to have positive radial entire solutions with prescribed asymptotic behavior at infinity we first study the upper and lower estimates for the nonlinear integral operator which is inverse of one dimensional polar form of the n dimensional m laplace operator

morse index and uniqueness for positive solutions of radial p laplace equations we study the positive radial solutions of the dirichlet problem p u f u 0 in b u 0 in b u 0 on b where p u div u p 2 u p 1 is the p laplace operator b is the unit ball in r n centered at the origin and f is a c 1 function we are able to get results on the spectrum of the linearized operator in a suitable weighted space of radial functions and derive from this information on the morse index in particular we show that positive radial solutions of mountain pass type have morse index 1 in the subspace of radial functions of w 1 p 0 b we use this to prove uniqueness and nondegeneracy of positive radial solutions when f is of the type u s u q and p 2

uniqueness theorems for negative radial solutions of k hessian equations in a ball abstract in this paper we apply a pohozaev type identity and the monotone separation techniques to prove the uniqueness of negative radial solutions of k hessian equations in a finite ball

lidstone polynomials and boundary value problems abstract we define lidstone polynomials provide their explicit representations give their relations with bernoulli polynomials obtain best possible error estimates in lidstone interpolation and establish several best possible sharp inequalities which compare favourably with the known results next we use these results to study even order differential equations together with lidstone boundary conditions

classical and non classical solutions of a prescribed curvature equation we discuss existence and multiplicity of positive solutions of the one dimensional prescribed curvature problem u root 1 u 2 lambda f t u u 0 0 u 1 0 depending on the behaviour at the origin and at infinity of the potential integral u 0 f t s ds besides solutions in w 2 w 1 0 1 we also consider solutions in w loc 2 1 0 1 which are possibly discontinuous at the endpoints of 0 1 our approach is essentially variational and is based on a regularization of the action functional associated with the curvature problem c 2007 elsevier inc all rights reserved

existence of multiple symmetric positive solutions of higher order lidstone problems this paper gives the sufficient conditions of the existence of at least three symmetric positive solutions for one type of higher order autonomous lidstone problem by applying the five functionals fixed point theorem the analogous result for higher order nonautonomous singular lidstone problem is also proved here

object pose from 2 d to 3 d point and line correspondences in this paper we present a method for optimally estimating the rotation and translation between a camera and a 3 d object from point and or line correspondences first we devise an error function and second we show how to minimize this error function the quadratic nature of this function is made possible by representing rotation and translation with a dual number quaternion we provide a detailed account of the computational aspects of a trust region optimization method this method compares favourably with newton s method which has extensively been used to solve the problem at hand with faugeras toscani s linear method faugeras and toscani 1986 for calibrating a camera and with the levenberg marquardt non linear optimization method finally we present some experimental results which demonstrate the robustness of our method with respect to image noise and matching errors

hyperbolic householder transformations a class of transformation matrices analogous to the householder matrices is developed with a nonorthogonal property designed to permit the efficient deletion of data from least squares problems these matrices which we term hyperbolic householder are shown to effect deletion or simultaneous addition and deletion of data with much less sensitivity to rounding errors than for techniques based on normal equations when the addition deletion sets are large this numerical robustness is obtained at the expense of only a modest increase in computations and when only a relatively small fraction of the data set is modified there is a decrease in required computations two applications to signal processing problems are considered first these transformations are used to obtain a square root algorithm for windowed recursive least squares filtering second the transformations are employed to implement the rejection of spurious data from the weight vector estimator in an adaptive array

exact number of solutions of a one dimensional prescribed mean curvature equation with concave convex nonlinearities abstract in this paper an exact number of solutions is obtained for the one dimensional prescribed mean curvature equation with concave convex nonlinearities in the form of u 1 u 2 u p u q u x 0 0 x 1 u 0 u 1 0 where 0 is a parameter and p q satisfy 0 p 1 q the arguments are based upon a time map method

positive versus compact support solutions to a singular elliptic problem abstract the semilinear elliptic problem u k x u q u p u 0 in u 0 on is considered in this paper where is a bounded domain of r n n 2 with c 2 boundary 0 q p 1 and k x as x we mainly study the effect of the blow up rate of k x near to the existence of positive and compact support solutions furthermore an optimal compact support principle is given for a class of elliptic differential inequalities

solutions of 2nth lidstone boundary value problems and dependence on higher order derivatives abstract in this paper we consider the lidstone boundary value problem 1 n u 2n x f x u x u x u 2 n 1 x 0 u 2i 0 u 2i 1 0 0 i n 1 some monotone conditions are imposed on f which enable us to apply a new maximum principle to deduce the existence of solution the emphasis here is that f depends on higher order derivatives two examples are also included to dwell upon the importance of the results obtained

exact multiplicity for some quasilinear elliptic dirichlet problems where the non linearity changes sign abstract the exact multiplicity of positive solutions is obtained for a class of quasilinear elliptic dirichlet problems where the non linearity changes sign meanwhile the uniqueness of positive ground state on r n is also obtained

fourth order criteria for blind sources separation various criteria based on contrast functions as well as higher order statistics are used for solving the problem of blind separation of sources in the paper for the case of instantaneous mixtures of two sources it is proved that the minimization or the cancellation of a really simple criterion a fourth order cross cumulant leads to a set of solutions whose spurious ones can be simply cancelled by using a decorrelation

multichannel blind separation of sources algorithm based on cross cumulant and the levenberg marquardt method we derive a new cost function that is more general than our previous one and is based on the cross cumulant 2 spl times 2 of the output signals however the new algorithm deals with multiple inputs and multiple outputs mimos and uses a levenberg marquardt method for the minimization of the cost function

indefinite weight nonlinear problems with neumann boundary conditions abstract we present a multiplicity result of positive solutions for the neumann problem associated with a second order nonlinear differential equation of the following form u a t g u 0 where the weight function a t has indefinite sign the only assumption we make for the nonlinear term g u is that its primitive g u presents some oscillations at infinity expressed by the condition involving lim g u u 2 0 lim g u u 2 as an application we obtain multiple radially symmetric solutions for neumann problems associated with u a x g u 0

a lower bound for the wehrl entropy of quantum spin with sharp high spin asymptotics a lower bound for the wehrl entropy of a single quantum spin is derived the high spin asymptotics of this bound coincides with lieb s conjecture up to but not including terms of first and higher order in the inverse spin quantum number the result presented here may be seen as complementary to the verification of the conjecture in cases of lowest spin by schupp commun math phys 207 481 1999 the present result for the wehrl entropy is obtained from interpolating a sharp norm bound that also implies a sharp lower bound for the so called renyi wehrl entropy with certain indices that are evenly spaced by half of the inverse spin quantum number

bifurcation of nodal radial solutions for a prescribed mean curvature problem on an exterior domain abstract we investigate the existence and multiplicity of nodal radial solutions for a prescribed mean curvature problem on the exterior domain of a ball using the global bifurcation theory moreover we establish the asymptotic behavior of the solutions on the subcontinua which bifurcate from a trivial branch all results are obtained by considering a radially equivalent second order problem with a singular weight

uniqueness of positive radial solutions for quasilinear elliptic equations in an annulus abstract extending a previous result of tang 1 we prove the uniqueness of positive radial solutions of p u f u 0 subject to dirichlet boundary conditions on an annulus in r n with 2 p n under suitable hypotheses on the nonlinearity f this argument also provides an alternative proof for the uniqueness of positive solutions of the same problem in a finite ball see 9 in the complement of a ball or in the whole space r n see 10 3 11

a compact support principle for singular elliptic differential inequalities with a gradient term abstract in this paper a compact support principle is established for the elliptic differential inequality u u p k x f u u 0 for x large where p 1 k x 0 and f satisfies conditions f1 f3 below the main feature of this note is the presence of the gradient term u p and the singular coefficient function k x the result is optimal in some sense related to the power p and the decaying rate of k x at and the proof is based on finding appropriate comparison functions we also give a similar result in a bounded domain of r n n 2

a direct solution for blind separation of sources proposes a direct estimation of the mixing matrix in the source separation problem as a new result we prove that for non gaussian sources the mixing matrix can be obtained by solving a fourth degree polynomial equation that derives from nonlinear equations only involving fourth order cumulants

pairs of positive radial solutions for a minkowski curvature neumann problem with indefinite weight abstract we prove the existence of a pair of positive radial solutions for the neumann boundary value problem div u 1 u 2 a x u p 0 in b u 0 on b where b is a ball centered at the origin a x is a radial sign changing function with b a x d x 0 p 1 and 0 is a large parameter the proof is based on the leray schauder degree theory and extends to a larger class of nonlinearities

a necessary and sufficient condition for 2nth order singular super linear m point boundary value problems abstract in this paper we study the existence of positive solutions for singular super linear m point boundary value problems of 2nth order ordinary differential equations a necessary and sufficient condition for the existence of c 2 n 2 0 1 positive solutions as well as c 2 n 1 0 1 positive solutions is given by means of the fixed point theorems on cones

global structure of radial positive solutions for a prescribed mean curvature problem in a ball abstract in this paper we are concerned with the global structure of radial positive solutions of boundary value problem div n v f x v 0 in b r v 0 on b r where n y y 1 y 2 y r n is a positive parameter b r x r n x r and denotes the euclidean norm in r n all results depending on the behavior of nonlinear term f near 0 are obtained by using global bifurcation techniques

positive periodic solutions to an indefinite minkowski curvature equation abstract we investigate the existence non existence multiplicity of positive periodic solutions both harmonic i e t periodic and subharmonic i e kt periodic for some integer k 2 to the equation u 1 u 2 a t g u 0 where 0 is a parameter a t is a t periodic sign changing weight function and g 0 0 is a continuous function having superlinear growth at zero in particular we prove that for both g u u p with p 1 and g u u p 1 u p q with 0 q 1 p the equation has no positive t periodic solutions for close to zero and two positive t periodic solutions a small one and a large one for large enough moreover in both cases the small t periodic solution is surrounded by a family of positive subharmonic solutions with arbitrarily large minimal period the proof of the existence of t periodic solutions relies on a recent extension of mawhin s coincidence degree theory for locally compact operators in product of banach spaces while subharmonic solutions are found by an application of the poincare birkhoff fixed point theorem after a careful asymptotic analysis of the t periodic solutions for

structure of boundary blow up solutions for quasi linear elliptic problems ii small and intermediate solutions the structure of positive boundary blow up solutions to quasi linear elliptic problems of the form pu f u u on 1 0 in z1 z2 large small and intermediate solutions are obtained for sufficiently large it is known from part i see structure of boundary blow up solutions for quasilinear elliptic problems part i large and small solutions preprint that the large solution is the unique large solution to the problem we will see that the small solution is also the unique small solution to the problem while there are infinitely many intermediate solutions our results are new even for the case p 2

positive solutions of nonlinear p laplacian equations in rn abstract this paper studies the existence of positive solutions of the nonlinear p laplacian equation p u f x u in r n existence of infinitely many positive solutions is established via super sub solution methods decaying conditions on f x u at x are imposed necessity of the conditions and nonexistence of positive solutions are illustrated through decay growth estimates of solutions at infinity special situation and examples are checked in detail

on sufficient conditions for the existence of radially symmetric solutions of the p laplace equation abstract we consider the dirichlet problem for the p laplace equation with a nonlinear source new a priori estimates for solutions are established in particular we obtain an explicit formula which shows the dependence of the existence of a weak bounded radially symmetric solution on the dimension of the problem

global bifurcation of solutions of the mean curvature spacelike equation in certain friedmann lemaitre robertson walker spacetimes abstract we study the existence of spacelike graphs for the prescribed mean curvature equation in the friedmann lemaitre robertson walker flrw spacetime by using a conformal change of variable this problem is translated into an equivalent problem in the lorentz minkowski spacetime then by using rabinowitz s global bifurcation method we obtain the existence and multiplicity of positive solutions for this equation with 0 dirichlet boundary condition on a ball moreover the global structure of the positive solution set is studied

nonexistence of positive radial solutions of a quasilinear neumann problem with a critical sobolev exponent note that problem 1 1 always admits the constant solution u0 k ny2 4 in adimurthi yadava 3 and budd knaap peletier 6 it has been proved that there exists a constant k0 0 such that for 0 k k0 1 1 admits a nonconstant solution for n 4 5 6 and does not for n 3 in this paper we study problem 1 1 when n 3 7 in this case the method used in 3 and 6 breaks down due to the fact that n 2 ny 2 2 which leads to a drastic change in the behaviour of the associated pohozhaev s functionals in contrast to the case n 4 5 6 we have

numerical solution of a class of singular free boundary problems involving the m laplace operator for a class of singular free boundary problems with applications in electromagnetism and plasma physics an analytical numerical approach is proposed based on the asymptotic expansion of the solution in the neighborhood of the singular points this approach was already used to approximate the solution of certain classes of singular boundary value problems on bounded lima and morgado 2009 14 and unbounded domains konyukhova et al 2008 12 here one parameter families of solutions of suitable singular cauchy problems describing the behavior of the solution at the singularities are derived and based on these families numerical methods for the approximation of the solution of the free boundary problems are constructed

uniqueness of positive solutions of δu f u 0 in ℝn n 3 we study the uniqueness of radial ground states for the semilinear elliptic partial differential equation delta u f u 0 eqno in n we assume that the function f has two zeros the origin and u 0 0 above u 0 the function f is positive is locally lipschitz continuous and satisfies convexity and growth conditions of a superlinear nature below u 0 f is assumed to be non positive non identically zero and merely continuous our results are obtained through a careful analysis of the solutions of an associated initial value problem and the use of a monotone separation theorem it is known that for a large class of functions f the ground states of are radially symmetric in these cases our result implies that possesses at most one ground state

monotonicity up to radially symmetric cores of positive solutions to nonlinear elliptic equations local moving planes and unique continuation in a non lipschitz case we prove local monotonicity and symmetry properties for nonnegative solutions of scalar field equations with nonlinearities which are not lipschitz our main tools are a local moving plane method and a unique continuation argument

asymptotic behavior of ground states of quasilinear elliptic problems with two vanishing parameters part iii abstract we study the asymptotic behavior of ground states of quasilinear elliptic problems with two vanishing parameters thanks to an additional fixed parameter we show that two different critical exponents play a crucial role in the asymptotic analysis giving an explanation of the phenomena discovered in gazzola et al asymptotic behavior of ground states of quasilinear elliptic problems with two vanishing parameters ann inst h poincare anal non lineaire to appear and gazzola and serrin ann inst h poincare anal non lineaire 19 2002 477

multiplicity results for sign changing bound state solutions of a semilinear equation abstract in this paper we give conditions on f so that the problem u f u 0 x r n n 2 has at least two radial bound state solutions with any prescribed number of zeros and such that u 0 belongs to a specific subinterval of 0 this property will allow us to give conditions on f so that this problem has at least any given number of radial solutions having a prescribed number of zeros

singular lidstone boundary value problem with given maximal values for solutions abstract the singular problem 1 nx 2n f t x x 2n 2 x 2j 0 x 2j t 0 0 j n 1 max x t 0 t t a depending on the parameter is considered here the positive caratheodory function f may be singular at the zero value of all its phase variables the paper presents conditions which guarantee that for any a 0 there exists a 0 such that the above problem with a has a solution x ac2n 1 0 t which is positive on 0 t the proofs are based on the regularization and sequential techniques and use the leray schauder degree and vitali s convergence theorem

ground states and free boundary value problems for the n laplacian in n dimensional space using a new gradient estimate we prove several theorems on the existence of radial ground states for the n laplace equation div u n 2 u f u 0 in rn n 1 and the existence of positive radial solutions for the associated dirichlet neumann free boundary value problem in a ball we treat exponentially subcritical critical and supercritical nonlinearities f u which also are allowed to have singularities at zero moreover we show that the local behavior of f at zero affects the existence in a crucial way this allows us to prove the existence of ground states for a large class of functions f u without imposing any restriction on their growth for large u

positive solutions for 2nth order singular sub linear m point boundary value problems abstract this paper investigates the existence of positive solutions for 2nth order singular sub linear m point boundary value problems firstly we establish a comparison theorem then we define a partial ordering in c2n 2 a b c2n a b and construct lower and upper solutions to give a necessary and sufficient condition for the existence of c2n 2 0 1 as well as c2n 1 0 1 positive solutions our nonlinearity f t x1 x2 xn may be singular at xi 0 i 1 2 n t 0 and or t 1

on radially symmetric minima of nonconvex functionals abstract we study a minimization problem in the space w1 10 br where br is the ball of radius r with center at the origin the functional considered is not necessarily convex under suitable assumptions we prove the existence of a radially symmetric decreasing solution by strengthening the assumptions we obtain uniqueness results finally we study under which assumptions and in which sense the solutions found solve the corresponding euler equation the proofs are very direct and simple they only make use of the functions t n introduced by the author arch rational mech anal 1999

on the existence of sign changing bound state solutions of a quasilinear equation abstract in this paper we establish the existence of bound state solutions having a prescribed number of sign changes for p m u f u 0 x r n n m 1 where m u u m 2 u our result is new even for the case of the laplacian m 2

existence of positive solutions of lidstone boundary value problems abstract we show that there exists at least one positive solution for lidstone boundary value problem 1 n u 2 n t f t u t u t u 2 n 1 t 0 t 1 u 2 i 0 u 2 i 1 0 i 0 1 n 1 under some suitable conditions our proof is based upon global bifurcation techniques

existence and uniqueness of solutions for a fourth order boundary value problem abstract in this paper we study the fourth order two point boundary value problem x t f t x t x t x t x t 0 t 0 1 x 0 x 1 0 a x 0 b x 0 0 c x 1 d x 1 0 by means of lower and upper solution method growth conditions on the nonlinear term f which guarantee the existence of solutions for the above boundary value problem are given in particular we obtain the uniqueness of the solution by imposing a monotone condition of the term f

spacelike hypersurfaces with prescribed boundary values and mean curvature we consider the boundary value problem for the mean curvature operator in minkowski space and give necessary and sufficient conditions for the existence of smooth strictly spacelike solutions our main results hold for non constant mean curvature and make no assumptions about the smoothness of the boundary or boundary data

on 2nth order lidstone boundary value problems this paper is concerned with the solutions of a class of 2nth order lidstone boundary value problems sufficient conditions for the existence and uniqueness of a solution are given a monotone iteration is developed so that the iteration sequence converges monotonically to a maximal or a minimal solution the approach to the problem is by the method of upper and lower solutions with a new maximum principle

positive radial solutions for dirichlet problems with mean curvature operators in minkowski space abstract in this paper by using leray schauder degree arguments and critical point theory for convex lower semicontinuous perturbations of c 1 functionals we obtain existence of classical positive radial solutions for dirichlet problems of type div v 1 v 2 f x v 0 in b r v 0 on b r here b r x r n x r and f 0 r 0 r is a continuous function which is positive on 0 r 0

positive radial solutions for multiparameter dirichlet systems with mean curvature operator in minkowski space and lane emden type nonlinearities abstract we deal with dirichlet systems involving the mean curvature operator in minkowski space m w div w 1 w 2 in a ball in r n using the fixed point index and the lower and upper solutions method we first obtain the existence of positive solutions for a class of differential systems with a singular laplacian subjected to homogeneous mixed boundary conditions the main application of the general results concerns dirichlet systems with lane emden type nonlinearities in a superlinear case depending on two parameters 1 2 so we prove that for such a system there exists a continuous curve which separates the first quadrant in two disjoint unbounded open sets o 1 and o 2 such that the system has zero at least one or at least two radial positive solutions according to 1 2 o 1 1 2 or 1 2 o 2

the strong maximum principle revisited in this paper we rst present the classical maximum principle due to e hopf together with an extended commentary and discussion of hopf s paper we emphasize the comparison technique invented by hopf to prove this principle which has since become a main mathematical tool for the study of second order elliptic partial dierential equations and has generated an enormous number of important applications while hopf s principle is generally understood to apply to linear equations it is in fact also crucial in nonlinear theories such as those under consideration here in particular we shall treat and discuss recent generalizations of the strong maximum principle and also the compact support principle for the case of singular quasilinear ellip tic dierential inequalities under generally weak assumptions on the quasilinear operators and the nonlinearities involved our principal interest is in necessary and sucient con ditions for the validity of both principles in exposing and simplifying earlier proofs of corresponding results and in extending the conclusions to wider classes of singular oper ators than previously considered the results have unexpected rami cations for other problems as will develop from the exposition e g i two point boundary value problems for singular quasilinear ordinary dierential equations sections 3 4 ii the exterior dirichlet boundary value problem section 5 iii the existence of dead cores and compact support solutions i e dead cores at in nity section 7 iv euler lagrange inequalities on a riemannian manifold section 9 v comparison and uniqueness theorems for solutions of singular quasilinear dierential inequalities section 10 the case of p regular elliptic inequalities is briesy considered in section 11

boundary value problems occurring in plate deflection theory abstract the paper deals with several iterative methods for solving some boundary value problems occurring in plate deflection theory making it possible to avoid the lengthy problem preparation which is required to solve these problems by finite difference methods

existence and uniqueness of positive solutions for a higher order boundary value problem the goal of this paper is to study the existence and uniqueness of positive solutions for the 2nth order boundary value problem 1 nu 2 n f t u u 1 n 1u 2 n 2 a 0u 2 i 0 email protected 0u 2 i 1 0 0 i 0 1 n 1 a 1u 2 i 1 email protected 1u 2 i 1 1 0 i 0 1 n 1 the krein rutman theorem and the krasnoselskii zabreiko fixed point theorem are the main tools that have been used to develop our work

multiple positive solutions of nonlinear two point boundary value problems we improve the results obtained by erbe hu and wang in a recent paper we show that there exist at least two positive solutions of two point boundary value problems under conditions weaker than those used by erbe hu and wang

glueing a peak to a non zero limiting profile for a critical moser trudinger equation abstract druet 6 proved that if f is a sequence of moser trudinger type nonlinearities with critical growth and if u solves 1 and converges weakly in h 0 1 to some u then the dirichlet energy is quantified namely there exists an integer n 0 such that the energy of u converges to 4 n plus the dirichlet energy of u as a crucial step to get the general existence results of 7 it was more recently proved in 8 that for a specific class of nonlinearities see 2 the loss of compactness i e n 0 implies that u 0 in contrast we prove here that there exist sequences f of moser trudinger type nonlinearities which admit a noncompact sequence u of solutions of 1 having a nontrivial weak limit

ground state solution for a problem with mean curvature operator in minkowski space abstract in this paper we prove the existence of a radial ground state solution for a quasilinear problem involving the mean curvature operator in minkowski space

nodal solutions for a sublinear elliptic equation we consider radial solutions of u u u 2 u 0 in rd with d 1 0 and prove by a shooting method the existence of compactly supported solutions with any given number of nodes

existence of positive solutions for 2nth order singular semipositone differential equations with sturm liouville boundary conditions abstract this paper studies a class of 2 n th order singular semipositone differential equations with sturm liouville boundary conditions some new results on the existence of c 2 n 2 0 1 positive solutions and c 2 n 1 0 1 positive solutions for this class of differential equations are derived we obtain some relations between the solutions and green s functions

positive solutions of a 2nth order boundary value problem involving all derivatives via the order reduction method this paper is mainly concerned with the existence multiplicity and uniqueness of positive solutions for the 2nth order boundary value problem 1 nu 2 n f t u u 1 i 2 u i 1 n 1u 2 n 1 u 2 i 0 u 2 i 1 1 0 i 0 1 n 1 where n 2 and f c 0 1 xr 2 n r r 0 we first use the method of order reduction to transform the above problem into an equivalent initial value problem for a first order integro differential equation and then use the fixed point index theory to prove the existence multiplicity and uniqueness of positive solutions for the resulting problem based on a priori estimates achieved by developing spectral properties of associated parameterized linear integral operators finally as a byproduct our main results are applied for establishing the existence multiplicity and uniqueness of symmetric positive solutions for the lidstone problem involving all derivatives

multiple solutions for neumann and periodic problems with singular ϕ laplacian abstract we use the critical point theory for convex lower semicontinuous perturbations of c 1 functionals to establish existence of multiple radial solutions for some one parameter neumann problems involving the operator v div v 1 v 2 similar results for periodic problems are also provided