positive solutions for singular semi positone boundary value problems in this paper some new results about the existence of positive solutions for singular semi positone boundary value problems are obtained the results of this paper partially improve the former corresponding work

the second expansion of the solution for a singular elliptic boundary value problem abstract in this paper we analyze the second expansion of the unique solution near the boundary to the singular dirichlet problem u b x g u u 0 x u 0 where is a bounded domain with smooth boundary in r n g c 1 0 0 g is decreasing on 0 with lim s 0 g s and g is normalised regularly varying at zero with index 1 b c is positive in may be vanishing on the boundary

rational double points on supersingular k3 surfaces we investigate configurations of rational double points with the total milnor number 21 on supersingular k3 surfaces the complete list of possible configurations is given as an application we also give the complete list of extremal quasi elliptic fibrations on supersingular k3 surfaces

structure of ground state solutions of singular semilinear elliptic equations abstract this paper deals with a class of singular semilinear elliptic equations in r n where the combined effects of a singular and a sublinear term allow us to establish some existence symmetry and uniqueness results for positive ground state solutions

supersingular k3 surfaces in odd characteristic and sextic double planes we show that every supersingular k3 surface is birational to a double cover of a projective plane

an exact estimate result for singular p laplacian equations with sign changing potential abstract in this paper we study the multiplicity of positive solutions for a singular p laplacian problem with sign changing potential by the nehari method and some analysis techniques we obtain two positive solutions and point out one of the two positive solutions is a ground state solution moreover we provide an exact estimate to ensure the singular p laplacian problem has two positive solutions

asymptotic behavior of entire large solutions to semilinear elliptic equations abstract in this paper by using karamata regular variation theory we study the exact asymptotic behavior of entire large solutions to u b x f u x r n n 3 where b c r n is nonnegative and nontrivial in r n f c 0 is positive and non decreasing on 0 which satisfies keller osserman condition and is rapidly varying or regularly varying at infinity with index 1

existence of solutions to some singular initial value problems on etudie l existence des solutions et leurs domaines de definition pour des problemes aux valeurs initiales pour des equations differentielles d ordre 1 et 2 qui sont singulieres soit dans les variables dependantes soit dans les variables independantes

boundary behaviour of the unique solution to a singular dirichlet problem with a convection term by karamata regular variation theory and constructing comparison functions we derive that the boundary behaviour of the unique solution to a singular dirichlet problem u b x g u u q u 0 x u 0 which is independent of u q w here is a bounded domain with smooth boundary in r n r q 0 2 lims 0 g s a ndb is nonnegative on which may be vanishing on the boundary

singular nonlinear boundary value problems for second order ordinary differential equations abstract the boundary value problem y f x y 0 y 0 y 0 0 y 1 y 1 0 is studied under conditions which are modeled on the problem y a x y p 0y 0 y 1 0 or y 0 y 1 0 which occurs in a number of applications the technical arguments involve properties of solutions i e concavity and the use of iterative techniques a new fixed point theorem for cones for decreasing mappings is proved and used it is of interest in its own right since most such theorems are for monotone increasing mappings

the exact boundary behavior of the unique solution to a singular dirichlet problem with a nonlinear convection term abstract in this paper we analyze the exact boundary behavior of the unique solution to the singular nonlinear dirichlet problem u b x g u u q u 0 x u 0 where is a bounded domain with smooth boundary in r n q 0 2 0 g c 1 0 0 lim s 0 g s g is decreasing on 0 and b c loc is positive in may be vanishing or singular on the boundary we reveal that the nonlinear convection term u q does not affect the first expansion of the unique solution near the boundary to the problem

a singular nonlinear boundary value problem membrane response of a spherical cap the nonlinear boundary value problem y n x 2 32y 2 lambda 2 8 quad 0 0 nu 0 are constants models the large deflection membrane response of a spherical cap and has been solved numerically by various techniques in the engineering literature we prove existence and uniqueness of a solution of this problem provide qualitative information about the solution and use this information to suggest an approach to numerical computation

existence and multiplicity of positive solutions for classes of singular elliptic pdes we consider the boundary value problem u g u u in u 0on where rn is a bounded domain is a nonnegative function in l such that 0 on some subset of of positive measure and g 0 r is continuous we establish the existence of three positive solutions when g 0 0 positone the graph of s 1g s is roughly s shaped and 0 we also prove that there exists at least one positive solution when g 0 0 and 0 1 we employ the method of sub super solutions to prove our results

boundary behavior for a singular quasi linear elliptic equation abstract we obtain the existence and uniqueness regularity and boundary behavior for a class of singular quasi linear elliptic equations in a smooth bounded domain

singular elliptic problems existence non existence and boundary behavior abstract we deal with the existence uniqueness and boundary behavior of positive solutions of the semilinear elliptic equation u a x g u b x f u in under dirichlet boundary conditions where r n is a bounded domain with smooth boundary a b g f are continuous non negative real valued functions the main feature here is that either g or f or both of them are singular at 0 in the sense that g t f t t 0 and 0 are parameters our results require no symmetry from either a or b and no monotonicity on f or g penalty arguments as well as variational principles are exploited

existence and multiplicity of positive solutions for neumann problems involving singularity and critical growth abstract in this paper the existence and multiplicity of positive solutions is established for a class of numann problems of the form u u 2 1 u in u 0 on here is a smooth bounded domain in r n n 3 2 2 n n 2 0 1 and 0 is a real parameter is the outer normal derivative the main technical approach is based on the variational and perturbation methods

the exact asymptotic behaviour of the unique solution to a singular nonlinear dirichlet problem abstract by karamata regular varying theory a perturbed argument and constructing comparison functions we show the exact asymptotic behaviour of the unique solution u c 2 c near the boundary to a singular dirichlet problem u b x g u f u u 0 x u 0 which is independent on f u and we also show the existence and uniqueness of solutions to the problem where is a bounded domain with smooth boundary in r n 0 g c 1 0 0 and there exists 1 such that lim t 0 g t g t 1 0 f c loc 0 0 the function f s s s 0 is decreasing on 0 for some s 0 0 and b is nonnegative nontrivial on which may be vanishing on the boundary

on the existence of positive solutions for some nonlinear elliptic problems in unbounded domain in r2 abstract we are interested in the following nonlinear elliptic equation u u u 0 in d where d is a smooth unbounded domain in r 2 under appropriate conditions on the nonlinearity x t related to a certain kato class we give some existence results and asymptotic behavior for positive solutions of the above equation

on ground state solutions for singular and semi linear problems including super linear terms at infinity abstract we establish a result concerning the existence of entire positive classical and bounded solutions which converge to zero at infinity for the semi linear equation u f x u x r n where f r n 0 0 is a suitable function and 0 is a real parameter this result completes the principal theorem of a mohammed a mohammed ground state solutions for singular semi linear elliptic equations nonlinear analysis 2008 doi 10 1016 j na 2008 11 080 mainly because his result does not address the super linear terms at infinity penalty arguments lower upper solutions and an approximation procedure will be used

an existence and uniqueness result for the singular lane emden fowler equation abstract using a fixed point theorem of general concave operators we present in this paper criteria which guarantee the existence and uniqueness of positive solutions for the singular lane emden fowler equation

eigenvalues and the one dimensional p laplacian we consider the boundary value problem p u f t u 0 with p 1 t 0 1 u 0 u 1 0 and with 0 the value of is chosen so that the boundary value problem has a positive solution in addition we derive an explicit interval for such that for any in this interval the existence of a positive solution to the boundary value problem is guaranteed in addition the existence of two positive solutions for in an appropriate interval is also discussed

combined effects of singular and superlinear nonlinearities in some singular boundary value problems abstract this paper deals with a class of singular semilinear elliptic dirichlet boundary value problems where the combined effects of a superlinear and a singular term allow us to establish some existence and multiplicity results

singular second order boundary value problems many other boundary conditions could be considered however since the analysis is similar we choose to omit the details for example if b denoted y 0 y 1 0 the results of this case follow from the results when b is denoted by i by making a change of variable problems of the form 1 l have been studied by a variety of authors see l 3 5 7 lo 141 for example the most advanced results to date seem to be those in 3 7 and 111 however in these papers f x y is decreasing in y for each x e 0 1 here we will not require this assumption for example we will show that y y o y 0 0 t 1 y 0 y 1 0 with 0 i 2 0 5 y 1 has a solution furthermore in fact in the case where f x y is decreasing in y our results improve those of 3 71 and 111 to show existence of a solution to 1 1 we will use the technique initiated in lo and ll the methods in those papers rely on the topological transversality theorem 8 91 the arzela ascoli theorem and apriori bounds on solutions

extremal discs and the regularity of cr mappings in higher codimension we develop a local theory of extremal analytic discs attached to a strictly pseudoconvex manifold of higher codimension in complex space we then apply the results to prove the regularity of cr homeomorphisms of such manifolds introduction in his celebrated paper lempert li introduced extremal analytic discs as geodesies of the kobayashi metric on a convex domain d c cn let a be the unit disc in the complex plane an analytic disc a d is called extremal if 0 attains its maximum among all analytic discs in d with the same values and directions at 0 g a extremal discs are important holomorphic invariants of d their boundaries lie in the boundary bd of the domain and form an invariant family of curves for the cr structure of bd lempert li l2 applies the extremal discs to the regularity of biholomorphic mappings monge amp re equations and normal forms of convex domains other applications include deformations and embeddibility of cr structures bl bd and polynomial hulls s

rational curves on the supersingular k3 surface with artin invariant 1 in characteristic 3 abstract we show the existence of 112 non singular rational curves on the supersingular k3 surface x with artin invariant 1 in characteristic 3 by several ways these non singular rational curves have the minimum degree with respect to a very ample divisor on x using these rational curves we have a 16 10 configuration and a 280 4 112 10 configuration on the k3 surface moreover we study the picard lattice by using the theory of the leech lattice the 112 non singular rational curves correspond to 112 leech roots

finite and infinite energy solutions of singular elliptic problems existence and uniqueness abstract we establish existence and uniqueness of solution for the homogeneous dirichlet problem associated to a fairly general class of elliptic equations modeled by u h u f in where f is an irregular datum possibly a measure and h is a continuous function that may blow up at zero we also provide regularity results on both the solution and the lower order term depending on the regularity of the data and we discuss their optimality

positive solutions to singular and non singular second order boundary value problems abstract the existence of positive solutions to second order singular boundary value problems is established our analysis is based on the topological transversality theorem of andrzej granas which relies on the notions of an essential map and a priori estimates on solutions

c i positive solutions of nonlinear singular differential equations for nonmonotonic function terms abstract suppose f t u v is nonnegative continuous on 0 1 r r and nondecreasing on u and nonincreasing on v for each fixed t there exist real numbers a 0 1 b 0 such that for any 0 r 1 f t r u v r a f t u v f t u r v r b f t u v u v r r then a necessary and sufficient condition for the boundary value problem u f t u u 0 0 t 1 u 0 u 0 0 u 1 u 1 0 to have c 0 1 positive solutions is that 0 0 1 g s s f s 1 1 d s where r 0 are nonnegative real numbers 0 and g t s is green s function of the above problem when f x u u 0

critical points and positive solutions of singular elliptic boundary value problems usually we do not think there is variational structure for singular elliptic boundary value problems so it cannot be considered by using critical points theory in this paper we use critical theory on certain convex closed sets to solve positive solutions for singular elliptic boundary value problems especially use the ordinary differential equation theory of banach spaces to obtain new results on the existence of multiple positive solutions the method is useful for other singular problems

existence of positive solutions to some singular and nonsingular second order boundary value problems abstract the topological transversality theorem is employed to study existence of solutions to a variety of singular and nonsingular second order boundary value problems of the form y f t y y 0 0 t t 0 t 1 y 0 and or y 0 the principal tools are the arzela ascoli theorem essential maps and a priori bounds on solutions

iterative solution for a singular nonlinear elliptic problem we consider the singular boundary value problem du q x u a p x u email protected u w 0 where 0 0 p x 0 and p x q x 0 and certain smoothness assumptions we show that there exists a unique classical positive solution u x c 2 m i n a c w c 1 r email protected 0

combined effects of singular and critical nonlinearities in elliptic problems abstract in this paper we consider the existence and multiplicity of positive weak solutions for a class of elliptic problems with the nonlinearity containing both singular and critical terms by means of the concentration compactness principle due to lions and ekeland s variational principle two positive weak solutions are obtained

ground state solutions for the singular lane emden fowler equation with sublinear convection term abstract we are concerned with singular elliptic equations of the form u p x g u f u u a in r n n 3 where p is a positive weight and 0 a 1 under the hypothesis that f is a nondecreasing function with sublinear growth and g is decreasing and unbounded around the origin we establish the existence of a ground state solution vanishing at infinity our arguments rely essentially on the maximum principle

new fixed point theorems for mixed monotone operators and local existence uniqueness of positive solutions for nonlinear boundary value problems abstract in this article we present a new fixed point theorem for a class of general mixed monotone operators which extends the existing corresponding results moreover we establish some pleasant properties of nonlinear eigenvalue problems for mixed monotone operators based on them the local existence uniqueness of positive solutions for nonlinear boundary value problems which include neumann boundary value problems three point boundary value problems and elliptic boundary value problems for lane emden fowler equations is proved the theorems for nonlinear boundary value problems obtained here are very general

solvability of some nonlinear boundary value problems on etablit l existence des solutions positives de problemes a deux points limites singuliers pour des equations differentielles de la forme y f t y y o o t 1

on singular semilinear elliptic equations abstract for the semilinear elliptic equation u p x u 0 x r n n 3 0 we show via the barrier method the existence of a positive entire solution behaving like x 2 n near

blow up boundary solutions of semilinear elliptic problems we consider the following semilinear elliptic equation u p x f u in u 0 u 0 in 1 where rn n 3 is a smooth domain bounded or possibly unbounded with compact possibly empty boundary we assume throughout this paper that p is a non negative function such that p c0 if is bounded and p c loc otherwise the nonlinearity f is assumed to ful ll f 1 f c1 0 f 0 f 0 0 and f 0 on 0 and the keller osserman condition see 7 13

classical and weak solutions of a singular semilinear elliptic problem the singular semilinear elliptic equation u p x f u 0 is shown to have a unique positive classical solution inrnthat decays to zero at ifp x is simply a nontrivial nonnegative continuous function satisfying 0 t max x t p x dt providedfis a non increasing continuously differentiable function on 0 it is also shown that the equation has a unique weakh10 solution on a bounded domain provided e0 f s ds andp x l2

c k regularity for the bar partial equation on strictly pseudoconvex domains with piecewise smooth boundarieson strictly pseudoconvex domains with piecewise smooth boundaries

distributional boundary values of holomorphic functions on product domains we show that holomorphic functions of polynomial growth on domains with corners have distributional boundary values in an appropriate sense provided the corners are generic cr manifolds we also prove an analog of the bochner hartogs theorem for these boundary values for the simplest such domains the product domains

boundary value problems for singular second order functional differential equations abstract we consider general linear boundary value problems for equations of the form y f x y x 0 0 x x is continuous and f x y has a singularity at y 0 the results improve and extend earlier results for the case x x due to taliaferro 1979 and gatica 1989

the existence and non existence of positive solutions to a singular quasilinear elliptic problem in rn abstract this paper deals with the existence and nonexistence of entire positive solutions of the quasilinear elliptic equation p u a x g u b x f u in r n 1 p n n 3 with u x 0 as x here either g or f or both of them are singular at 0 in the sense that g t f t as t 0 by using a perturbation method which eliminates the singularity on a ball with radius r and then let r tends to infinity with help of the bounded super solution of the original problem we obtain the existence of a weak solution of the problem the main results of this paper improve the corresponding results of dragos patru covei the existence and asymptotic behavior of a positive solution to a quasilinear elliptic problem in r n nonlinear anal 69 2008 2615 2622 j v goncalves c a santos singular elliptic problems existence non existence and boundary behavior nonlinear anal 66 2007 2078 2090

iterative methods for a singular boundary value problem we consider a second order nonlinear ordinary differential equation of the form y 1 q xy q 0 x 1 where q 0 with the boundary conditions y 0 y 1 0 this problem arises in boundary layer equations for the flow of a power law fluid over an impermeable semi infinite flat plane we show that classical iterative schemes such as the picard and newton methods converge to the solution of this problem in spite of the singularity of the solution if we choose an adequate initial approximation moreover we observe that these methods are more efficient than the methods used before and may be applied to a larger range of values of q numerical results for different values of q are given and compared with the results obtained by other authors

minimax methods for singular elliptic equations with an application to a jumping problem abstract a jumping problem for a class of singular semilinear elliptic equations is considered minimax methods in the framework of nonsmooth critical point theory are applied

positive solutions of the p laplace equation with singular nonlinearity abstract for a given bounded domain in r n with c 1 boundary for some 0 1 and a possibly singular nonlinearity f on 0 we give sufficient conditions on f so that the p laplace equation p u f x u admits a solution u w 0 1 p on the basis of a comparison principle we will give a sufficient condition under which such a problem admits a unique solution

on the superlinear ambrosetti prodi problem l et be a smooth bounded domain in r n we consider the semilinear elliptic boundary value problem

monotone positive solutions for singular boundary value problems consider the nonlinear scalar differential equations 1 p t p t y t sign 1 q t f t y t p t y t 0 where 0 1 p and q are singular at t 0 1 and f c 0 1 r r r associated to boundary conditions y 0 limt 0 p t y t 0 0 limt 1 p t y t limt 0 p t y t existence of a monotone positive solutions of this bvp are given with their slope a priori bounded under superlinear or sublinear growth in f the approach is based on the analysis of the corresponding vector field on the face plane and the well known shooting technique

projective models of the supersingular k3 surface with artin invariant 1 in characteristic 5 abstract let x be a supersingular k3 surface in characteristic 5 with artin invariant 1 then x has a polarization that realizes x as the fermat sextic double plane we present a list of polarizations of x with degree 2 whose intersection number with this fermat sextic polarization is less than or equal to 5 and give the defining equations of the corresponding projective models we also present a method to describe birational morphisms between these projective models explicitly as a by product a non projective automorphism of the fermat sextic double plane is obtained

boundary regularity of proper holomorphic mappings it s main result is formulated in theorem 2 below although the answer to the conjecture in the general case is still unknown it has been shown to hold in many special cases a fairly detailed history of this subject will be contained in 14 one class of positive answers deals with cases in which one knows that f21 and 2 posses fairly large classes of holomorphic automorphisms that extend holomorphically across the boundaries like for instance reinhardt domains see e g h cartan 8 w kaup 16 and st bell 6 in these situations one even often does not need a smoothness assumption on the boundaries of 1 and 22 on the other hand the first result without a priori knowledge on automorphisms which gave c extendability was proved by ch fefferman in 1974 in 15 and says

existence of explosive positive solutions of quasilinear elliptic equations abstract in this paper our main purpose is to consider the quasilinear equation div u p 2 u m x f u on a domain r n n 3 where f is a nonnegative nondecreasing continuous function which vanishes at the origin and m is a nonnegative continuous function with the property that any zero of m is contained in a bounded domain in such that m is positive on its boundary for bounded we show that a nonnegative solution u satisfying u x as x exists for un boundary including r n we show that a similar result holds where u x as x within and u x as x

positive solution of a singular non linear elliptic boundary value problem the singular elliptic boundary value problem du g x u a h x u b 0in w u 0in w u 0on wis considered in this paper where a 0 1 b 0 w is a bounded region in r n with a smooth boundary under a set of suitable assumptions including that h x 0 in w and suppg supph it is proved that there exists a classic solution u and when g x 0 or g x 0 in whole w then the solution u is unique

on dirichlet problems with singular nonlinearity of indefinite sign abstract let be a smooth bounded domain in r n n 1 let k m be two nonnegative functions and let 0 we study existence and nonexistence of positive solutions for singular problems of the form u k x u m x u in u 0 on where 0 is a real parameter we mention that as a particular case our results apply to problems of the form u m x u in u 0 on where m is allowed to change sign in

the asymptotic behaviour of the unique solution for the singular lane emden fowler equation abstract by karamata regular variation theory and constructing comparison functions we show the exact asymptotic behaviour of the unique classical solution u c 2 c near the boundary to a singular dirichlet problem u k x g u u 0 x u 0 where is a bounded domain with smooth boundary in r n g c 1 0 0 lim t 0 g t g t for each 0 for some 0 and k c loc for some 0 1 is nonnegative on which is also singular near the boundary

existence uniqueness and multiplicity of positive solutions for schrodinger poisson system with singularity abstract in this paper we consider the following schrodinger poisson system with singularity u u u r in u 2 in u 0 in u 0 on where r 3 is a smooth bounded domain with boundary 1 r 0 1 is a constant 0 is a parameter we obtain the existence and uniqueness of positive solution for 1 and any 0 by using the variational method the existence and multiplicity of solutions for the system are also considered for 1 and 0 small enough by using the method of nehari manifold

a boundary value problem for normalized finsler infinity laplacian equations with singular nonhomogeneous terms abstract we study boundary value problems of finsler infinity laplacian equations with nonhomogeneous terms that may exhibit singularity when solutions vanish on the boundary