a priori bounds and multiplicity for fully nonlinear equations with quadratic growth in the gradient abstract we consider fully nonlinear uniformly elliptic equations with quadratic growth in the gradient such as f x u d u d 2 u c x u m x d u d u h x in a bounded domain with a dirichlet boundary condition here r c h l p p n 1 c 0 and the matrix m satisfies 0 1 i m 2 i recently this problem was studied in the coercive case c 0 where uniqueness of solutions can be expected and it was conjectured that the solution set is more complex for noncoercive equations this conjecture was verified in 2015 by arcoya de coster jeanjean and tanaka for equations in divergence form by exploiting the integral formulation of the problem here we show that similar phenomena occur for general even fully nonlinear equations in nondivergence form we use different techniques based on the maximum principle we develop a new method to obtain the crucial uniform a priori bounds which permit to us to use degree theory this method is based on basic regularity estimates such as half harnack inequalities and on a vazquez type strong maximum principle for our kind of equations

quasilinear elliptic equations and weighted sobolev poincare inequalities with distributional weights abstract we introduce a class of weak solutions to the quasilinear equation p u u p 2 u in an open set r n with p 1 where p u u p 2 u is the p laplacian operator our notion of solution is tailored to general distributional coefficients which satisfy the inequality h p d x h p h p d x for all h c 0 here 0 and 0 p 1 2 p if p 2 or 0 1 if 0 p 2 as we shall demonstrate these conditions on are natural for the existence of positive solutions and cannot be relaxed in general furthermore our class of solutions possesses the optimal local sobolev regularity available under such a mild restriction on we also study weak solutions of the closely related equation p v p 1 v p under the same conditions on our results for this latter equation will allow us to characterize the class of satisfying the above inequality for positive and thereby extending earlier results on the form boundedness problem for the schrodinger operator to p 2

existence results for a class of nonlinear elliptic problems with p growth in the gradient abstract we prove the existence of bounded solutions for a class of nonlinear elliptic problems whose model is in the form div a x u du k 1 u du p k 2 u f u w 0 1 p l where a x b p b is a continuous monotone decreasing function and k1 and k2 are continuous monotone increasing functions

singular quasilinear equations with quadratic growth in the gradient without sign condition given a bounded domain in r n a nd af unctiona l q with q n 2 we study the existence of a positive solution for the quasilinear problem

compact operators into the spaces of strongly c1 summable and bounded sequences abstract we establish the necessary and sufficient conditions for the entries of an infinite matrix to map any of the classical sequence spaces l p 1 p c 0 and c into the spaces w 0 w and w of all sequences that are strongly summable to zero strongly summable and strongly bounded by the cesaro method of order 1 we also give the representations of the general bounded linear operators from c into any of the spaces w 0 w and w and compute or estimate the hausdorff measure of noncompactness in each case finally we apply our results to characterise the compact linear operators between the spaces mentioned above and generalise two classical results by steinhaus 1911 5 maddox 1967 31 and cohen and dunford 1937 24

uniqueness and the maximum principle for quasilinear elliptic equations with quadratic growth conditions in this paper we show that the maximum principle holds for quasilinear elliptic equations with quadratic growth under general structure conditions

origins of the limited information maximum likelihood and two stage least squares estimators theil basmann and sargan are often credited with the development of the two stage least squares tsls estimator of the coefficients of one structural equation in a simultaneous equations model however anderson and rubin had earlier derived the asymptotic distribution of the limited information maximum likelihood liml estimator by finding the asymptotic distribution of what is essentially the tsls estimator

comparison results and improved quantified inequalities for semilinear elliptic equations in this paper we prove some pointwise comparison results between the solutions of some second order semilinear elliptic equations in a domain omega of mathbb r n and the solutions of some radially symmetric equations in the equimeasurable ball omega the coefficients of the symmetrized equations in omega satisfy similar constraints as the original ones in omega we consider both the case of equations with linear growth in the gradient and the case of equations with at most quadratic growth in the gradient moreover we show some improved quantified comparisons when the original domain is not a ball the method is based on a symmetrization of the second order terms

some new sequence spaces derived by the domain of generalized difference matrix let l denote any one of the classical spaces c c 0 and p of bounded convergent null and absolutely p summable sequences respectively and l also be the domain of the generalized difference matrix b r s in the sequence space l where 1 p the present paper is devoted to studying on the sequence space l furthermore the b and c duals of the space l are determined and the schauder bases for the spaces c c 0 and p are given and some topological properties of the spaces c 0 1 and p are examined finally the classes l 1 l 2 and l 1 l 2 of infinite matrices are characterized where l 1 c c 0 p 1 and l 2 c c 0 1

matrix transformations between the sequence spaces w 0 p λ v 0 p λ c 0 p λ 1 p and certain bk spaces in this paper we determine the b duals of the sets w 0 p l v 0 p l and c 0 p l for exponentially bounded email protected furthermore we characterize matrix transformations between the sequence spaces w 0 p l v 0 p l c 0 p l 1

existence and comparison results for quasilinear elliptic equations with critical growth in the gradient abstract we give a condition of existence of bounded solutions for a general quasilinear elliptic problem with quadratic growth in the gradient when the data are small enough moreover we obtain an a e comparison with the semilinear symmetrized problem

on compact operators and some euler b m difference sequence spaces abstract altay and basar 2005 1 and altay basar and mursaleen 2006 2 introduced the euler sequence spaces e 0 t e c t and e t basarir and kayikci 2009 3 defined the b m difference matrix and studied some topological and geometric properties of some generalized riesz b m difference sequence space in this paper we introduce the euler b m difference sequence spaces e 0 t b m e c t b m and e t b m consisting of all sequences whose b m transforms are in the euler spaces e 0 t e c t and e t respectively moreover we determine the and duals of these spaces and construct the schauder basis of the spaces e 0 t b m and e c t b m finally we characterize some matrix classes concerning the spaces e 0 t b m and e c t b m and give the characterization of some classes of compact operators on the sequence spaces e 0 t b m and e t b m

continuum of solutions for an elliptic problem with critical growth in the gradient abstract we consider the boundary value problem p u h 0 1 l u c x u x u 2 h x where r n n 3 is a bounded domain with smooth boundary it is assumed that c 0 c h belong to l p for some p n 2 and that l we explicitly describe a condition which guarantees the existence of a unique solution of p when 0 and we show that these solutions belong to a continuum the behaviour of the continuum depends in an essential way on the existence of a solution of p 0 it crosses the axis 0 if p 0 has a solution otherwise it bifurcates from infinity at the left of the axis 0 assuming that p 0 has a solution and strengthening our assumptions to x 1 0 and h 0 we show that the continuum bifurcates from infinity on the right of the axis 0 and this implies in particular the existence of two solutions for any 0 sufficiently small

generalization of the sequence space l p derived by weighted mean abstract the sequence space l p was introduced and studied by maddox i j maddox spaces of strongly summable sequences quart j math oxford 2 18 1967 345 355 in the present paper the sequence spaces l u v p of non absolute type which is derived by the generalized weighted mean is defined and proved that the spaces l u v p and l p are linearly isomorphic besides this the and duals of the space l u v p are computed and the basis of that space is constructed further it is established that the sequence space l p u v has ad property and given f dual of the space l p u v finally the matrix mappings from the sequence spaces l u v p to the sequence space and from the sequence space to the sequence space l u v p are characterized

applications of the hausdorff measure of noncompactness in some sequence spaces of weighted means in the present paper we establish some identities or estimates for the operator norms and the hausdorff measures of noncompactness of certain operators on some sequence spaces of weighted means furthermore by using the hausdorff measure of noncompactness we apply our results to characterize some classes of compact operators on those spaces

nonlinear elliptic equations with natural growth in the gradient and source terms in lorentz spaces abstract in this paper we consider the problem u w 0 1 p div a x u d u b x u d u h x u d u in d where div a x u d u is a leray lions operator which is defined on w 0 1 p with coercivity where the growth with respect to du of h x u d u is controlled by d u p and where b x u d u satisfies a similar growth condition but has the good sign the main feature of the problem is that the source terms belong to the lorentz space l n p when two smallness conditions are satisfied the second one depends on the behavior of b x u d u when u tends to infinity we prove the existence of a solution which further satisfies e p 1 u 1 w 0 1 p for every with 0 for some threshold 0 the key ingredient in the proof of the existence result is an a priori estimate which holds true for every solution to the problem which satisfies the above mentioned exponential regularity condition

compactness of matrix operators on some new difference sequence spaces abstract the difference sequence spaces c 0 and l have recently been introduced by mursaleen and noman 2010 m mursaleen a k noman on some new difference sequence spaces of non absolute type math comput modelling 52 3 4 2010 603 617 in the present paper we establish some identities or estimates for the operator norms and the hausdorff measures of noncompactness of certain matrix operators on the spaces c 0 and l further by using the hausdorff measure of noncompactness we characterize some classes of compact operators on these spaces

reduced rank regression for blocks of simultaneous equations abstract reduced rank regression analysis provides maximum likelihood estimators of a matrix of regression coefficients of specified rank and of corresponding linear restrictions on such matrices these estimators depend on the eigenvectors of an effect matrix in the metric of an error covariance matrix in this paper it is shown that the maximum likelihood estimator of the restrictions can be approximated by a function of the effect matrix alone the procedures are applied to a block of simultaneous equations the block may be over identified in the entire model and the individual equations just identified within the block the procedures are generalizations of the limited information maximum likelihood and two stage least squares estimators

on the b difference sequence space derived by generalized weighted mean and compact operators abstract in the present paper by using generalized weighted mean and difference matrix b we introduce the paranormed sequence space l u v p b which consist of all sequences whose generalized weighted b difference means are in the linear space l p introduced by i j maddox also we give the basis of this space and compute its and duals further we characterize the classes of matrix mappings from l u v p b to l c and c 0 finally we apply the hausdorff measure of noncompactness to characterize some classes of compact operators given by matrices on the space l p u v b 1 p

on the euler sequence spaces which include the spaces lp and l ii abstract by e p r we mean the space of all sequences whose euler transforms of order r are in the sequence spaces l p and l see b altay f basar m mursaleen on the euler sequence spaces which include the spaces l p and l i inform sci 2005 in press where 1 p in the present paper we essentially characterize the classes e p r l e 1 r l p and e p r f of infinite matrices for 1 p and give the characterizations of some other matrix mappings from the space e p r to the euler riesz difference etc sequence spaces by means of a given basic lemma we devote the final section of the paper to examining some geometric properties of the space e p r

compact operators on the spaces a0r δ and acr δ abstract in c aydin f basar some new difference sequence spaces appl math comput 157 2004 677 693 aydin and basar introduced the new difference sequence spaces a c r and a 0 r and characterized the classes a c r l p and a c r c here we characterize the subclasses k x y of compact operators where x is a c r and y is one of the spaces c 0 c l l 1 b v by applying the hausdorff measure of noncompactness

on generalized means and some related sequence spaces in the present paper we introduce the notion of generalized means and define some related sequence spaces which include the most known sequence spaces as special cases further we study some topological properties of the spaces of generalized means and construct their bases finally we determine the b duals of these spaces and characterize some related matrix classes

matrix transformations between sequence spaces of generalized weighted means the main object of this paper is to introduce and study some sequence spaces which arise from concept of weighted means determine their b duals and characterize matrix transformations between them

a priori estimates and bifurcation of solutions for an elliptic equation with semidefinite critical growth in the gradient abstract we study nonnegative solutions of the boundary value problem p u c x u x u 2 h x u h 0 1 l where is a smooth bounded domain of r n c l h l r for some r n 2 and c h 0 our main motivation is to study the semidefinite case namely unlike in previous work on the subject we do not assume to be uniformly positive in nor even positive everywhere in space dimensions up to n 5 we establish uniform a priori estimates for weak solutions of p when 0 is bounded away from 0 this is proved under the assumption that the supports of and c intersect a condition that we show to be actually necessary and in some cases we further assume that is uniformly positive on the support of c and or some other conditions as a consequence of our a priori estimates assuming that p 0 has a solution we deduce the existence of a continuum c of solutions such that the projection of c onto the axis is an interval of the form 0 a for some a 0 and that the continuum c bifurcates from infinity to the right of the axis 0 in particular for each 0 small enough problem p has at least two distinct solutions

existence and uniqueness for several non linear elliptic problems arising in lubrication theory we consider the non linear elliptic equation a x p p b x p with positive dirichlet boundary data the coefficients a and b are taken from models used in lubrication theory andin particular are not d negative values of p we prove some general existence anduniqueness results for a family of mod els which extendrelatedresults in the literature these results allow us to prove existence uniqueness andpositivity of the solution to advanced compressible lubrication models such as the kinetic based fukui kaneko model and the second order slip model we also consider a spring like model of compliant foil compressible bearing andweaken some hypotheses of previous results on more classical mod els such as the standard reynolds model and the first order slip model

the hausdorff measure of noncompactness of operators on the matrix domains of triangles in the spaces of strongly c 1 summable and bounded sequences in 2 3 7 the authors studied spaces of strongly c 1 summable and bounded sequences and matrix domains of triangles in them here we will extend their results by characterizing compact matrix operators from those spaces into the spaces of null and convergent sequences and by giving sufficient conditions for the compactness of the operators when the final space is the space of bounded sequences this is achieved by determining or estimating the hausdorff measure of noncompactness of such matrix operators

some new difference sequence spaces the difference sequence spaces d c d and c 0 d were studied by kizmaz canad math bull 24 2 1981 169 the sequence spaces a 0 r and a c r have been recently defined and examined by aydin and basar in hokkaido math j in press the main purpose of the present paper is to introduce the spaces a r 0 d and a r c d of difference sequences moreover it is proved that the spaces a r 0 d and a r c d are the bk spaces including the spaces c 0 and c and some inclusion relations have been given it is also proved that the sequence space a 0 r has ad property while the space a 0 r d has not furthermore the basis and the a b and c duals of the spaces a r 0 d and a r c d have been determined the last section of the paper has been devoted to theorems on the characterizations of the matrix classes a r c d p and a r c d c and the characterizations of some other matrix classes have been obtained by means of a given basic lemma where 1

a note on compact operators on matrix domains abstract we establish some identities or estimates for the operator norms and hausdorff measures of noncompactness of linear operators given by infinite matrices that map the matrix domains of triangles in arbitrary bk spaces with ak or in the spaces of all convergent or bounded sequences into the spaces of all null convergent or bounded sequences or of all absolutely convergent series furthermore we apply these results to the characterizations of compact operators on the matrix domains of triangles in the classical sequence spaces and on the sequence spaces studied in i djolovic compact operators on the spaces a 0 r and a c r j math anal appl 318 2 2006 658 666 i djolovic on the space of bounded euler difference sequences and some classes of compact operators appl math comput 182 2 2006 1803 1811

nonlinear fractional laplacian problems with nonlocal gradient terms let n 2 be a smooth bounded domain for s 1 2 1 we consider a problem of the form where 0 is a real parameter f belongs to a suitable lebesgue space and is a nonlocal gradient square term given by depending on the real parameter 0 we derive existence and non existence results the proof of our existence result relies on sharp calderon zygmund type regularity results for the fractional poisson equation with low integrability data we also obtain existence results for related problems involving different nonlocal diffusion terms

existence and non existence of solutions to elliptic equations with a general convection term in this paper we consider the nonlinear elliptic problem u u g u h x in u 0 on where is a smooth bounded domain of n 0 g is an arbitrary c 1 increasing function and h c 1 is non negative we completely analyse the existence and non existence of positive classical solutions in terms of the parameter we show that there exist solutions for every when 0 and the integral 1 g s d s or when 0 and the integral s g s d s conversely when the respective integrals converge and h is non trivial on existence depends on the size of moreover non existence holds for large our proofs mainly rely on comparison arguments and on the construction of suitable supersolutions in annuli our results include some cases where the function g is superquadratic and existence still holds without assuming any smallness condition on

on the euler sequence spaces which include the spaces l p and l i in the present paper we introduce the euler sequence space e p r consisting of all sequences whose euler transforms of order r are in the space p of non absolute type which is the bk space including the space p and prove that the spaces e p r and p are linearly isomorphic for 1

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

rearrangement relatif dans les equations elliptiques quasi lineaires avec un second membre distribution application a un theoreme d existence et de regularite abstract in this paper we are concerned with quasilinear elliptic equations that is p au f u u t in r u w01 p l where a is an operator of leray lions type which is defined on w 0 1 p l 1 f is a non linear map having a suitable growth and t is a distribution of w 1 r r n p 1 and r p p 1 using the techniques of the relative rearrangement ann scuola norm sup pisa cl sci 4 in press we give a precise a priori estimate of the solution u of p in l norm these estimates allow us to prove an existence theorem for p and to get the holder continuity of the solution u

solvability of uniformly elliptic fully nonlinear pde we get existence uniqueness and non uniqueness of viscosity solutions of uniformly elliptic fully nonlinear equations of the hamilton jacobi bellman isaacs type with unbounded ingredients and quadratic growth in the gradient without hypotheses of convexity or properness some of our results are new even for equations in divergence form

nonlinear elliptic equations and intrinsic potentials of wolff type abstract we give necessary and sufficient conditions for the existence of weak solutions to the model equation p u u q on r n in the case 0 q p 1 where 0 is an arbitrary locally integrable function or measure and p u div u u p 2 is the p laplacian sharp global pointwise estimates and regularity properties of solutions are obtained as well as a consequence we characterize the solvability of the equation p v b v p v on r n where b 0 these results are new even in the classical case p 2 our approach is based on the use of special nonlinear potentials of wolff type adapted for sublinear problems and related integral inequalities it allows us to treat simultaneously several problems of this type such as equations with general quasilinear operators div a x u fractional laplacians or fully nonlinear k hessian operators

some generalizations of the space b vp of p bounded variation sequences the spaces bvp and bv of sequences of p bounded variation have recently been introduced by basar and altay f basar b altay on the space of sequences of p bounded variation and related matrix mappings ukrainian math j 55 1 2003 136 147 where 1 p in the present paper the sequence spaces bv u p and bv u p of non absolute type have been defined and it has been proved that the spaces bv u p and bv u p are linearly isomorphic to the spaces l p and l p of maddox respectively besides this the and duals of the spaces bv u p and bv u p have been computed and the basis of the space bv u p has been constructed the classes bv u p l and bv u p c of infinite matrices have been characterized and the characterizations of some other classes have also been derived by means of a given basic lemma the final section of the paper has been devoted to some consequences about the rotundity of the space bv u p

applications of measure of noncompactness in operators on the spaces sα s0α s c α lpα abstract in this paper we characterize some operators and matrix transformations in the sequence spaces s s 0 s c l p moreover using the hausdorff measure of noncompactness necessary and sufficient conditions are formulated for a linear operator between the mentioned spaces to be compact among other things some results of cohen and dunford are recovered

a semilinear elliptic pde not in divergence form via variational methods in this paper we consider a semilinear equation driven by an operator not in divergence form precisely the principal part of the operator is in divergence form but it has also a lower order term depending on du while the right hand side of the equation satisfies superlinear and subcritical growth conditions at zero and at infinity the problem has not a variational structure but despite that we use variational techniques in order to prove an existence and regularity result for the equation

matrix transformations and compact operators on some new mth order difference sequences abstract we define some new sets of sequences the m th order differences of which are bounded convergent and convergent to zero and apply the general methods in e malkowsky v rakocevic on matrix domains of triangles appl math comput 189 2 2007 1146 1163 to give schauder bases for the latter two determine their duals and characterize matrix transformations on them our results generalize those in b de malafosse the banach algebra s and applications acta sci math szeged 70 1 2 2004 125 145 and improve those in e malkowsky s d parashar matrix transformations in spaces of bounded and convergent difference sequences of order m analysis 17 1997 87 97 we also establish identities and estimates for the hausdorff measure of non compactness of matrix operators from our spaces into the spaces of bounded convergent and null sequences and characterize the respective classes of compact operators some of these results generalize those in e malkowsky v rakocevic the measure of non compactness of linear operators between spaces of m th order difference sequences stud sci math hungar 33 1999 381 391

hausdorff measure of noncompactness of certain matrix operators on the sequence spaces of generalized means abstract in the present paper we derive some identities or estimates for the operator norms and the hausdorff measures of noncompactness of certain matrix operators on the sequence spaces of generalized means further by applying the hausdorff measure of noncompactness we obtain the necessary and sufficient conditions for such operators to be compact

measure of noncompactness of matrix operators on some difference sequence spaces of weighted means for a sequence x x k we denote the difference sequence by dx x k x k 1 let u u k k 0 and v v k k 0 be the sequences of real numbers such that u k 0 v k 0 for all email protected n the difference sequence spaces of weighted means l u v d are defined as l u v d x x k w x email protected where l c c 0 and and the matrix w w n k is defined by w n k u n v k v k 1 kn in this paper we establish some identities or estimates for the operator norms and the hausdorff measures of noncompactness of certain matrix operators on l u v d further we characterize some classes of compact operators on these spaces by using the hausdorff measure of noncompactness

good lambda and muckenhoupt wheeden type bounds in quasilinear measure datum problems with applications weighted good lambda type inequalities and muckenhoupt wheeden type bounds are obtained for gradients of solutions to a class of quasilinear elliptic equations with measure data such results are obtained globally over sufficiently flat domains in mathbb r n in the sense of reifenberg the principal operator here is modeled after the p laplacian where for the first time singular case frac 3n 2 2n 1 p le 2 frac 1 n is considered those bounds lead to useful compactness criteria for solution sets of quasilinear elliptic equations with measure data as an application sharp existence results and sharp bounds on the size of removable singular sets are deduced for a quasilinear riccati type equation having a gradient source term with linear or super linear power growth

some remarks on elliptic problems with critical growth in the gradient abstract in this work we analyze existence nonexistence multiplicity and regularity of solution to problem 1 u u u 2 f x in u 0 on where is a continuous nondecreasing positive function and f belongs to some suitable lebesgue spaces

banach algebras of matrix transformations between some sequence spaces related to λ strong convergence and boundedness we study the spaces c 0 l c l and c l of sequences that are l strongly convergent to zero l strongly convergent and l strongly bounded and the related spaces v 0 l and v l in particular we give the characterizations of several classes of matrix transformations between those spaces furthermore we use our results to prove that the classes of matrix transformations from v l c l and c l into themselves are banach algebras as an application of our results we establish an estimate for the hausdorff measure of noncompactness of matrix operators that map c l into itself give a characterization of the subclass of compact operators and a sufficient condition for those operators to be fredholm

on matrix domains of triangles we prove some general results for the determination of the duals of and the characterisations of matrix transformations on matrix domains of arbitrary triangles in fk spaces our results contain almost all recently published ones as special cases we also study the measure of noncompactness of several matrix transformations in particular we obtain some known results of sember give the corrected version of a recent result by djolovic and study compact operators on some spaces of altay basar and mursaleen

applications of measures of noncompactness to the infinite system of differential equations in lp spaces abstract in this paper we apply the technique of measures of noncompactness to the theory of infinite system of differential equations in the banach sequence spaces l p 1 p our aim is to present some existence results for infinite system of differential equations formulated with the help of measures of noncompactness

some paranormed sequence spaces of non absolute type derived by weighted mean abstract the sequence spaces l p c p and c 0 p were introduced and studied by maddox i j maddox paranormed sequence spaces generated by infinite matrices proc cambridge philos soc 64 1968 335 340 in the present paper the sequence spaces u v p of non absolute type which are derived by the generalized weighted mean are defined and proved that the spaces u v p and p are linearly isomorphic where denotes the one of the sequence spaces l c or c 0 besides this the and duals of the spaces u v p are computed and the basis of the spaces c 0 u v p and c u v p is constructed additionally it is established that the sequence space c 0 u v has ad property and given the f dual of the space c 0 u v p finally the matrix mappings from the sequence spaces u v p to the sequence space and from the sequence space to the sequence spaces u v p are characterized

compactness by the hausdorff measure of noncompactness abstract in the present paper we establish some identities or estimates for the operator norms and the hausdorff measures of noncompactness of certain operators given by infinite matrices that map an arbitrary b k space into the sequence spaces c 0 c l and l 1 and into the matrix domains of triangles in these spaces furthermore by using the hausdorff measure of noncompactness we apply our results to characterize some classes of compact operators on the b k spaces