combinatorial interior point methods for generalized network flow problems we present combinatorial interior point methods for the generalized minimum cost flow and the generalized circulation problems based on wallacher and zimmermann s combinatorial interior point method for the minimum cost network flow problem the algorithms have features of both a combinatorial algorithm and an interior point method they work towards optimality by iteratively reducing the value of a potential function while maintaining interior point solutions at each iteration flow is augmented along a generalized circulation which is computed by solving a tvpi two variables per inequality system the algorithms run in time where m and n are respectively the number of arcs and nodes in the graph and l is the length of the input data

classical solutions of singular monge ampere equations in a ball abstract our concern is on existence uniqueness and regularity of convex negative radially symmetric classical solutions to det d 2 u x u in b u 0 on b where d 2 u is the hessian of u b r n n 1 is the unit ball with boundary b b 0 0 is continuous and x t x t where x is the euclidean norm of x the main interest is in the case is singular at x 1 and or u 0 although several nonsingular cases are covered by the main result our approach to show existence exploits fixed point arguments and the shooting method uniqueness and regularity are achieved through suitable estimates

temporal constraint networks abstract this paper extends network based methods of constraint satisfaction to include continuous variables thus providing a framework for processing temporal constraints in this framework called temporal constraint satisfaction problem tcsp variables represent time points and temporal information is represented by a set of unary and binary constraints each specifying a set of permitted intervals the unique feature of this framework lies in permitting the processing of metric information namely assessments of time differences between events we present algorithms for performing the following reasoning tasks finding all feasible times that a given event can occur finding all possible relationships between two given events and generating one or more scenarios consistent with the information provided we distinguish between simple temporal problems stps and general temporal problems the former admitting at most one interval constraint on any pair of time points we show that the stp which subsumes the major part of vilain and kautz s point algebra can be solved in polynomial time for general tcsps we present a decomposition scheme that performs the three reasoning tasks considered and introduce a variety of techniques for improving its efficiency we also study the applicability of path consistency algorithms as preprocessing of temporal problems demonstrate their termination and bound their complexities

boundary estimates of solutions for a class of monge ampere equations abstract on a smooth strictly convex bounded domain in r 2 we establish some boundary estimates of the solution to the complete hyperbolic affine sphere equation on the unit ball in r n we also give some sharp estimates of the solutions of a class of monge ampere equations as an application we prove the relative hyperbolic hypersurface constructed by solving two linked monge ampere equations has constant gauss kronecker curvature and has bounded principal curvatures

existence non existence and asymptotic behavior of blow up entire solutions of semilinear elliptic equations abstract we are mainly concerned with existence non existence and the behavior at infinity of non negative blow up entire solutions of the equation u x f u in r n no monotonicity condition is assumed upon f and in fact we obtain solutions with a prescribed behavior both at infinity and at the origin the method used to get existence is based upon lower and upper solutions techniques while for non existence we explore radial symmetry estimates on an associated integral equation and the keller osserman condition

output feedback stabilization for a class of stochastic time delay nonlinear systems this note focuses on a class of stochastic time delay nonlinear systems the problem we address is to design a controller such that the closed loop system is exponentially stable it is shown that the stabilization via output feedback can be solved by a lyapunov based recursive design method

boundary behavior of solutions of monge ampere equations with singular righthand sides abstract in this paper by karamata regular variation theory and constructing super and subsolutions we obtain the asymptotic boundary behavior of convex solutions of monge ampere equations with singular righthand sides

on adaptive control of nonlinearly parameterized nonlinear systems towards a constructive procedure abstract a new framework to design immersion and invariance adaptive controllers for nonlinearly parameterized nonlinear systems was recently proposed by the authors the key step is the construction of a monotone mapping via a suitable selection of a controller tuning function which has to satisfy some integrability conditions this translates into the need to solve a partial differential equation pde in this paper this result is extended providing some answers to the questions of characterization of monotonizable systems and solvability of the pde first adding to the design a nonlinear dynamic scaling we obviate the need to solve the pde second for the case of factorizable nonlinearities the following results are established i it is shown that the monotonicity condition is satisfied if a linear matrix inequality is feasible ii directly verifiable involutivity conditions that ensure the solution of the pde are presented iii an explicit formula for the required tuning function is given provided the regressor matrix satisfies some rank conditions hence adding a dynamic scaling this yields a constructive solution to the problem

boundary blow up solutions for a class of elliptic equations on a bounded domain this paper deals with existence of solutions of the quasilinear elliptic equation du f x u u in w satisfying the boundary blow up condition u x x email protected where email protected r n is a bounded domain with smooth boundary email protected our main result applies to the existence of blow up solutions of a class of equations which appear in stochastic control theory namely du a x g u email protected u email protected x in w where a x g u j x are suitable functions and l s are nonnegative constants our approach employs an approximation procedure combined with both a non monotone iteration variant of the method of lower and upper solutions and fixed point arguments

querying temporal and spatial constraint networks in ptime we start with the assumption that temporal and spatial knowledge usually captured by constraint networks can be represented and queried more effectively by using the scheme of indefinite constraint databases because query evaluation in this scheme is in general a hard computational problem we seek tractable instances of query evaluation we assume that we have a class of constraints c with some reasonable computational and closure properties the computational properties of interest are that the satisfiability problem and an appropriate version of the variable elimination problem for c should be solvable in ptime under this assumption we exhibit general classes of indefinite constraint databases and first order modal queries for which query evaluation can be done with ptime data complexity we then search for tractable instances of c among the subclasses of horn disjunctive linear constraints over the rationals from previous research we know that the satisfiability problem for horn disjunctive linear constraints is solvable in ptime but not the variable elimination problem thus we try to discover subclasses of horn disjunctive linear constraints with tractable variable elimination problems the class of utvpi constraints is the largest class that we show to have this property finally we restate our general tractability results with c ranging over the newly discovered tractable classes interesting tractable query answering problems for indefinite temporal and spatial constraint databases are identified in this way we close our complexity analysis by precisely outlining the frontier between tractable and possibly intractable query answering problems

the dirichlet problem for nonlinear second order elliptic equations i monge ampegre equation on considere le probleme de dirichlet pour des equations elliptiques non lineaires pour une fonction reelle u definie dans la fermeture d un domaine borne dans r n avec une frontiere c

testing the necklace condition for shortest tours and optimal factors in the plane a tour of a finite set p of points is a necklace tour if there are disks with the points in p as centers such that two disks intersect if and only if their centers are adjacent in it has been observed by sanders that a necklace tour is an optimal traveling salesman tour

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

a polynomial combinatorial algorithm for generalized minimum cost flow we propose the first combinatorial solution to the generalized minimum cost flow problem flow with losses and gains despite a rich history dating back to kantorovich and dantzig until now the only known way to solve the problem in polynomial time was via general purpose linear programming techniques polynomial combinatorial algorithms were previously known only for the version of our problem without costs we design the first such algorithms for the version with costs our algorithms also find provably good solutions faster than optimal ones providing the first strongly polynomial approximation schemes for the problem our techniques extend to optimize linear programs with two variables per inequality polynomial combinatorial algorithms were previously developed for testing the feasibility of such linear programs we propose the first such methods for the optimization version

adaptive feedback control of nonlinear time delay systems the lasalle razumikhin based approach this note presents a new method to design adaptive feedback controller for nonlinear time delay systems first by using the lasalle razumikhin theorem a sufficient condition is derived that ensures the convergence of a part of the solution with stability for a class of functional differential equations then using this condition the adaptive stabilization problem is solved for nonlinear time delay systems moreover it is shown that for a class of nonlinear time delay systems with triangular structure the adaptive stabilizing controller can be obtained by recursively constructing the lyapunov razumikhin function it will be shown that the provided recursive design approach which is obviously motivated by the typical backstepping method is not a trivial extension of the existing design method

fast and simple approximation schemes for generalized flow we present fast and simple fully polynomial time approximation schemes fptas for generalized versions of maximum flow multicommodity flow minimum cost maximum flow and minimum cost multicommodity flow we extend and refine fractional packing frameworks introduced in fptas s for traditional multicommodity flow and packing linear programs our fptas s dominate the previous best known complexity bounds for all of these problems some by more than a factor of n2 where n is the number of nodes this is accomplished in part by introducing an efficient method of solving a sequence of generalized shortest path problems our generalized multicommodity fptas s are now as fast as the best non generalized ones we believe our improvements make it practical to solve generalized multicommodity flow problems via combinatorial methods

existence and uniqueness of nontrivial radial solutions for k hessian equations abstract we prove existence and uniqueness of nontrivial radial solutions to the k hessian problem s k d 2 u f u in u 0 on where s k d 2 u is the k hessian operator of u is the open unit ball in r n f is a continuous function and may have k sublinear growth at with possible k superlinear growth at 0 and is a large parameter

towards a genuinely polynomial algorithm for linear programming a linear programming algorithm is called genuinely polynomial if it requires no more than p m n arithmetic operations to solve problems of order m times n where p is a polynomial it is not known whether such an algorithm exists we present a genuinely polynomial algorithm for the simpler problem of solving linear inequalities with at most two variables per inequality the number of operations required is o mn 3 log text m the technique used was developed in a previous paper where a novel binary search idea was introduced

boundary behavior of large solutions to the monge ampere equations with weights abstract this paper is concerned with the monge ampere equation det d 2 u x b x f u x x where is a strictly convex bounded smooth domain in r n with n 2 and b c which is positive in but may be vanishing on the boundary we find a new structure condition on f which plays a crucial role in the boundary behavior of strictly convex large solutions our results are obtained in a more general setting than those in cirstea and trombetti 2008 12 where f is regularly varying at infinity with index p n

on singular boundary value problems for the monge ampere operator abstract we consider different types of singular boundary value problems for the monge ampere operator the approach is based on existing regularity theory and a subsolution supersolution method nonexistence and uniqueness results are also given

existence and estimates of solutions to a singular dirichlet problem for the monge ampere equation given a strictly convex smooth and bounded domain in rn we establish the existence of a negative convex solution in c c with zero boundary value to the singular monge ampere equation det d2u p x g u an associated dirichlet problem will be employed to provide a necessary and sufficient condition for the solvability of the singular boundary value problem estimates of solutions will also be given and regularity of solutions will be deduced from the estimates

alternating two way ac tree automata we explore the notion of alternating two way tree automata modulo the theory of finitely many associative commutative ac symbols this was prompted by questions arising in cryptographic protocol verification in particular in modeling group key agreement schemes based on diffie hellman like functions where the emptiness question for intersections of such automata is fundamental this also has independent interest we show that the use of general push clauses or of alternation leads to undecidability already in the case of one ac symbol with only functions of arity zero on the other hand emptiness is decidable in the general case of several function symbols including several ac symbols provided push clauses are unconditional and intersection clauses are final this class of automata is also shown to be closed under intersection

singular boundary value problems for the monge ampere equation abstract given a strictly convex smooth and bounded domain in r n we consider solving the monge ampere equation det d 2 u f x u for solutions in c c with zero boundary value where the nonlinearity f x t could be singular at t 0 we will show that under some fairly general assumptions on f the above dirichlet problem admits a negative convex solution in uniqueness of such solutions is then established for a wide class of nonlinearities f x t as a consequence of a comparison principle

boundary behavior of k convex solutions for singular k hessian equations abstract we discuss the existence and boundary behavior of k convex solution to the singular k hessian problem s k d 2 u x b x f u x x u x 0 x where s k d 2 u k 1 2 n is the k hessian operator r n n 2 is a smooth bounded strictly convex domain here the weight function b x is not necessarily bounded on another interest is that f u as u 0 our approach mainly relies on karamata s regular variation theory and the construction of suitable sub and super solutions

parameter estimation and compensation in systems with nonlinearly parameterized perturbations we consider a class of systems influenced by perturbations that are nonlinearly parameterized by unknown constant parameters and develop a method for estimating the unknown parameters the method applies to systems where the states are available for measurement and perturbations with the property that an exponentially stable estimate of the unknown parameters can be obtained if the whole perturbation is known the main contribution is to introduce a conceptually simple modular design that gives freedom to the designer in accomplishing the main task which is to construct an update law to asymptotically invert a nonlinear equation compensation for the perturbations in the system equations is considered for a class of systems with uniformly globally bounded solutions for which the origin is uniformly globally asymptotically stable when no perturbations are present we also consider the case when the parameters can only be estimated when the controlled state is bounded away from the origin and show that we may still be able to achieve convergence of the controlled state we illustrate the method through examples and apply it to the problem of downhole pressure estimation during oil well drilling

existence of entire explosive positive solutions of quasi linear elliptic equations in this paper our main purpose is to establish the existence of entire explosive positive radial solutions for quasi linear elliptic equations the main results of the paper extend previously known results both for the super linear and sub linear cases

memoryless state feedback controller design for time delay systems with matched uncertain nonlinearities the robust control problem for a class of uncertain time delay systems is investigated the systems include multiple time delays and uncertain nonlinear functions to our best knowledge no controller design method for the systems is reported in the literature except for sliding mode control smc however the sliding mode controller must use the delayed state of the system so that the precise time delays have to be known and also a large memory is needed for controller implementation to overcome the shortcomings we employ the backstepping method to design a memoryless state feedback controller by constructing a novel lyapunov krasovskii functional we show that the resulting closed loop system is asymptotically stable simulations are done to verify the effectiveness of the proposed method

boundary blow up solutions to the k hessian equation with a weakly superlinear nonlinearity abstract by constructing new sub and super solutions we are concerned with determining values of for which there exist k convex solutions to the boundary blow up k hessian problem s k d 2 u x h x u x k ln u x 0 for x u x as dist x 0 here k 1 2 n s k d 2 u is the k hessian operator 0 and is a smooth bounded strictly convex domain in r n n 2 we suppose that the nonlinearity behaves like u k ln u as u which is more complex and difficult to deal with than the nonlinearity grows like u p with p k or faster at infinity further several new results of nonexistence global estimates and estimates near the boundary for the solutions are also given

existence of positive boundary blow up solutions for quasilinear elliptic equations via sub and supersolutions abstract in this paper the existence of positive boundary blow up weak solution for the quasilinear elliptic equation div u p 2 u m x f u in a smooth bounded domain r n or global space r n are obtained under new conditions our proof is based on the method of sub and supersolutions

deciding linear inequalities by computing loop residues v r pratt has shown that the real and integer feastbdlty of sets of linear mequallues of the form x y c can be decided quickly by examining the loops m certain graphs pratt s method is generahzed first to real feaslbdlty of mequahues m two variables and arbitrary coefficients and ultimately to real feaslbdlty of arbitrary sets of hnear mequahtles the method is well suited to apphcatlons m program verification

existence of large solutions for a class of quasilinear elliptic equations abstract we consider the quasilinear elliptic equation div u p 2 u a x f u u 0 in where p 1 a x 0 a x 0 a x c and f is continuous and non decreasing on 0 satisfies f 0 0 f s 0 for s 0 and the keller osserman condition 1 f s 1 p d s f s 0 s f t d t we establish conditions on the function a that are necessary and sufficient for the existence of positive solutions bounded and unbounded of the given equation

a strongly polynomial algorithm for a special class of linear programs we extend the list of linear programming problems that are known to be solvable in strongly polynomial time to include a class of lps which contains special cases of the generalized transshipment problem the result is facilitated by exploiting some special properties associated with leontief substitution systems and observing that a feasible solution to the system ax b x 0 in which no variable appears in more than two equations can be found in strongly polynomial time for b belonging to some set

immersion and invariance adaptive control of nonlinearly parameterized nonlinear systems a new framework to design adaptive controllers for nonlinearly parameterized systems is proposed in this technical note the key step is the construction of a monotone mapping which explicitly depends on some of the estimator tuning parameters convexity that is related to monotonicity has been explored by several authors the property is assumed a priori and is useful for the design only in some region of state space which is completed switching the controller in our approach monotonicity can be used in the whole state space and moreover is enforced by the designer effectively becoming a synthesis tool one consequence of these features is that the controller does not rely on state dependent switching in order to dispose of degrees of freedom to render the function monotone we depart from standard adaptive control and adopt instead the recently introduced immersion and invariance approach

large solutions to the monge ampere equations with nonlinear gradient terms existence and boundary behavior abstract in this paper we obtain conditions about the existence and boundary behavior of strictly convex solutions to the monge ampere equations with boundary blow up det d 2 u x b x f u x u q x u and det d 2 u x b x f u x 1 u q x u where is a strictly convex bounded smooth domain in r n with n 2 q 0 n or q 0 n b c which is positive in but may vanish or blow up on the boundary f c 0 f 0 0 and f is strictly increasing on 0 or f c r f s 0 s r and f is strictly increasing on r

the linear complementarity problems with a few variables per constraint in this paper we consider the sparse linear complementarity problem denoted by k lcp the coefficient matrices are restricted to have at most k nonzero entries per row it is known that the 1 lcp is solvable in linear time and the 3 lcp is strongly np hard we show that the 2 lcp is strongly np hard and it can be solved in polynomial time if it is sign balanced i e each row of the matrix has at most one positive and one negative entry our second result matches the currently best known complexity bound for the corresponding sparse linear feasibility problem in addition we show that an integer variant of the sign balanced 2 lcp is weakly np hard and pseudo polynomially solvable and the generalized 1 lcp is strongly np hard

boundary blow up solutions to the k hessian equation with singular weights abstract in this paper we study the k convex solutions to the boundary blow up k hessian problem s k d 2 u h x u p for x u x as dist x 0 here k 1 2 n s k d 2 u is the k hessian operator and is a smooth bounded strictly convex domain in r n n 2 we show the existence nonexistence uniqueness results global estimates and estimates near the boundary for the solutions our approach is largely based on the construction of suitable sub and super solutions

adaptive control of nonlinearly parameterized systems the smooth feedback case studies global adaptive control of nonlinearly parameterized systems with uncontrollable linearization using a parameter separation technique and the tool of adding a power integrator we develop a feedback domination design approach for the explicit construction of a smooth adaptive controller that solves the problem of global state regulation in contrast to the existing results in the literature a key feature of our adaptive regulator is its minimum order property namely no matter how big the number of unknown parameters is the order of the dynamic compensator is identical to one and is therefore minimal as a consequence global state regulation of feedback linearizable systems with nonlinear parameterization is achieved by one dimensional adaptive controllers without imposing any extra e g convex concave conditions on the unknown parameters

delay identification for a class of nonlinear systems abstractthe problem of state estimation for nonlinear systems with unknown state delays is still an open problem in this paper we propose to add a delay identifier to suitable high gain observers in order to achieve simultaneous estimation of state and delay in the case of one constant delay in the state we provide sufficient conditions to guarantee the exponential convergence to zero of the errors globally with respect to the initial choice of the system state variables and locally with respect to the initial delay estimation we validate the method through an example concerning chaotic oscillators

existence of large solutions for quasilinear elliptic problems with a gradient term abstract in this paper we prove the existence of the positive large solutions for the equation div u m 2 u x u m 1 x u x in the whole space r n n 3 where 0 0 is a continuous function and m 1 with r n 0 0 is required to satisfy some hypotheses detailed blow more precisely we will give a sufficient and necessary condition for the existence of an entire large radial solution and a necessary condition for the existence of the entire large positive radial solution

nonlinear elliptic equations with singular boundary conditions abstract we consider the model problem formula where is a bounded region in r n with smooth boundary q 0 2 and k u u p p 1 or e u we show that there exists a classical solution

optimal global and boundary asymptotic behavior of large solutions to the monge ampere equation abstract this paper is mainly concerned with optimal global and boundary asymptotic behavior of strict convex large solutions to the monge ampere equation det d 2 u b x f u x where is a strict convex and bounded smooth domain in r n with n 2 f c 1 0 or f c 1 r which is increasing in 0 or r and satisfies the keller osserman type condition b c is positive in but may vanish or blow up on the boundary properly we find new structure conditions on f which play a crucial role in both global and boundary behavior of such solutions moreover we reveal asymptotic behavior of such solutions when the parameters on b tend to the corresponding critical values in addition when f does not satisfy the keller osserman type condition and is a ball we supply a necessary and sufficient condition on b for the existence of an infinitude of strict convex radially symmetric positive solutions to such problem

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

improved algorithms for linear inequalities with two variables per inequality the authors show that a system of m linear inequalities with n variables where each inequality involves at most two variables can be solved in tilde o mn 2 time we denote tilde o f o f polylog n polylog m deterministically and in tilde o n 3 mn expected time using randomization parallel implementations of these algorithms run in tilde o n time where the deterministic algorithm uses tilde o mn processors and the randomized algorithm uses tilde o n 2 m processors the bounds significantly improve over previous algorithms the randomized algorithm is based on novel insights into the structure of the problem

fuzzy approximation based adaptive control of strict feedback nonlinear systems with time delays this paper focuses on the problem of adaptive control for a class of nonlinear time delay systems with unknown nonlinearities and strict feedback structure based on the lyapunov krasovskii functional approach a state feedback adaptive controller is constructed by backstepping the proposed adaptive controller guarantees that the system output converges into a small neighborhood of the reference signal and all the signals of the closed loop system remain bounded compared with the results that exist the main advantage of the proposed method is that the controller design is independent of the choice of the fuzzy membership functions therefore a priori knowledge of fuzzy approximators is not necessary for control design and the proposed approach requires only one adaptive law for an nth order system two numerical examples are used to illustrate the effectiveness of the proposed approach

the existence and asymptotic behavior of boundary blow up solutions to the k hessian equation abstract in this paper we consider the existence and asymptotic behavior of k convex solution to the boundary blow up k hessian problem s k d 2 u h x f u for x u x as dist x 0 where k 1 2 n s k d 2 u is the k hessian operator is a smooth bounded strictly convex domain in r n n 2 h c is positive in but is not necessarily bounded on and f is a smooth positive function that satisfies the so called keller osserman condition further results are obtained for the special case that is a ball our approach to show the existence and asymptotic behavior exploits the method of sub and super solutions and karamata regular variation theory

constraint propagation with interval labels abstract constraint propagation is often used in ai systems to perform inference about quantities this paper studies one particular kind of constraint propagation where quantities are labelled with signs or with intervals and these labels are propagated through recorded constraints we review the uses of such inference schemes in ai systems of various kinds and evaluate their strengths and weaknesses in particular we determine the completeness and running time of constraint propagation for various kinds of labels and constraints

existence and boundary asymptotic behavior of large solutions of hessian equations abstract in this paper we establish the existence of large solutions of hessian equations and obtain a new boundary asymptotic behavior of solutions

on a k hessian equation with a weakly superlinear nonlinearity and singular weights abstract consider the existence nonexistence and global estimates of k convex solutions to the boundary blow up k hessian problem s k d 2 u x h x u x k ln u x 0 for x u x as dist x 0 here k 1 2 n s k d 2 u is the k hessian operator 0 is a smooth bounded strictly convex domain in r n n 2 and h x is a positive weight function which is singular near the boundary we first give the existence and nonexistence results of k convex solution to the above boundary blow up problem on a larger range of h and then we show that there is a k convex solution provided that h x grows fast near and u k ln u grows slow at it turns out that this case is more difficult to handle than the case in which h x grows slow near and u k ln u grows fast at this needs some new ingredients in the arguments

adaptive control of nonlinear time delay systems with application to a two stage chemical reactor global adaptive regulation of general strict feedback system with unknown time delay by state feedback is a long standing problem this note provides for the first time a solution to this problem by introducing a novel dynamic gain based adaptive backstepping approach a key feature of the developed approach is that the lyapunov function and the adaptive law are chosen in a new recursive manner with the help of appropriate lyapunov krasovskii functionals a memoryless state feedback controller is explicitly constructed it is shown that global adaptive regulation can be achieved for the nonlinear time delay system finally we use a two stage chemical reactor to demonstrate the application of the proposed scheme

existence and boundary behavior of solutions of hessian equations with singular right hand sides abstract in this paper we establish the existence of viscosity solutions of hessian equations with singular right hand sides and obtain the asymptotic boundary behavior of solutions the asymptotic results generalize those for poisson equations and monge ampere equations and are more precise than obtained from hopf lemma

large solution of a semilinear elliptic problem we show that large positive solutions exist for the following email protected u q p x f u p in w r n n 3 in which the domain w is either bounded or equal to r n the nonnegative function p is continuous and may vanish on large parts of w if w r n then p must satisfy a decay email protected 0 email protected r dr furthermore we show that the given conditions on p are nearly optimal for equation p

uniqueness of boundary blowup solutions to k curvature equation abstract we consider the boundary blowup problem for the k curvature equation i e h k u f u g d u in an n dimensional domain with the boundary condition u x as dist x 0 we prove the uniqueness result under some hypotheses