positive solutions for a class of multiparameter ordinary elliptic systems abstract using a fixed point theorem due to m a krasnosel skii the upper lower solutions method and fixed point index theory we study existence non existence and multiplicity of positive solutions for a class of systems of second order ordinary differential equations we give a new notion of superlinearity for nonlinearities observe that the nonlinearities may even be in some sense singular as an application we show multiplicity results for a class of semilinear elliptic systems in both bounded annular domains and exterior domains in addition we apply our results to fourth order boundary value problems

nonlinear bvps with functional parameters article history received 29 may 2007 available online 6d ecember 2008 msc primary 35j65 34b15 secondary 49j40 49j60 we study the existence nonexistence and properties of solutions for a certain class of second order odes and their dependence on functional parameters also in the case when nonlinearities are in some sense singular this approach is based on variational methods and cover both sublinear and superlinear cases we develop a duality theory and variational principles for this problem as a consequence of the duality theory we give a numerical version of the variational principle which enables approximation of the solution for our problem we apply these results to obtain the existence of bounded radial and positive classical solutions for the bvp of elliptic type observe that our method allows us to investigate a certain class of elliptic systems in both bounded

on a thin film model with insoluble surfactant abstract this paper studies the existence and asymptotic behavior of global weak solutions for a thin film equation with insoluble surfactant under the influence of gravitational capillary and van der waals forces we prove the existence of global weak solutions for medium sized initial data in large function spaces moreover exponential decay towards the flat equilibrium state is established where an estimate on the decay rate can be computed explicitly

characterizing diagnoses and systems abstract most approaches to model based diagnosis describe a diagnosis for a system as a set of failing components that explains the symptoms in order to characterize the typically very large number of diagnoses usually only the minimal such sets of failing components are represented this method of characterizing all diagnoses is inadequate in general in part because not every superset of the faulty components of a diagnosis necessarily provides a diagnosis in this paper we analyze the concept of diagnosis in depth exploiting the notions of implicate implicant and prime implicate implicant we use these notions to consider two alternative approaches for addressing the inadequacy of the concept of minimal diagnosis first we propose a new concept that of kernel diagnosis which is free of this problem with minimal diagnosis this concept is useful to both the consistency and abductive views of diagnosis second we consider restricting the axioms used to describe the system to ensure that the concept of minimal diagnosis is adequate

on generalized horn formulas and k resolution abstract a hierarchy of classes h k of propositional formulas has been introduced by yamasaki and doshita 1983 and gallo and scutella 1988 the classes h k have polynomially solvable satisfiability problem and the basic class is the set of horn formulas we show that the k resolution is complete and sound for h k where k resolution is a restriction of ordinary resolution in that at least one of the parent clauses has at most k literals furthermore we discuss to what extent the class of unsatisfiable formulas in h k and the class of unsatisfiable formulas for which a k resolution refutation exists coincide

positive solutions for superlinear elliptic equations the existence of a positive radial solution for superlinear elliptic boundary value problem in an exterior domain is proved by the use of cone expansion fixed point theorem

on the existence of bounded positive solutions for a class of singular bvps abstract we investigate the existence and properties of solutions to a second order singular ode we base ourselves on the variational approach which enables the approximation of solutions and gives a measure of a duality gap between primal and dual functional for minimizing sequences

existence of positive solutions for singular boundary value problems involving the one dimensional p laplacian this paper studies the existence of positive solutions for singular dirichlet boundary value problems these results are obtained by using the global continuation theorem fixed point index theory and approximate method

positive solutions of singular sublinear emden fowler boundary value problems abstract this paper is about the dirichlet boundary value problem of singular sublinear emden fowler equations a necessary and sufficient condition for the existence of positive solutions to this problem has been obtained by using the method of lower and upper solutions the uniqueness of positive solutions has also been discussed

extended horn sets in propositional logic the class of horn clause sets in propositional logic is extended to a larger class for which the satisfiability problem can still be solved by unit resolution in linear time it is shown that to every arborescence there corresponds a family of extended horn sets where ordinary horn sets correspond to stars with a root at the center these results derive from a theorem of chandresekaran that characterizes when an integer solution of a system of inequalities can be found by rounding a real solution in a certain way a linear time procedure is provided for identifying hidden extended horn sets extended horn but for complementation of variables that correspond to a specified arborescence finally a way to interpret extended horn sets in applications is suggested

multiple solutions for equations involving bilinear coercive and compact forms with applications to differential equations abstract the existence of multiple fixed points for the coercive bilinear compact forms defined in the cone in the banach space is proved multiple applications to the integral equations derived from bvps for differential equations are provided

on functional dependencies in q horn theories this paper studies functional dependencies in q horn theories and discusses their use in knowledge condensation we introduce compact model based representations of q horn theories analyze the structure of functional dependencies in q horn theories and show that every minimal functional dependency in a q horn theory can be expressed either by a single term or by a single clause we also prove that the set of all minimal functional dependencies in is quasi acyclic we then develop polynomial time algorithms for recognizing whether a given functional dependency holds in a q horn theory which is represented either by a q horn cnf or as the q horn envelope of a set of models finally we show that every q horn theory has a unique condensation and can be condensed in polynomial time

the motion of a thin liquid film driven by surfactant and gravity we investigate wave solutions of a lubrication model for surfactant driven flow of a thin liquid film down an inclined plane we model the flow in one space dimension with a system of nonlinear pdes of mixed hyperbolic parabolic type in which the effects of capillarity and surface diffusion are neglected numerical solutions reveal distinct patterns of waves that are described analytically by combinations of traveling waves some with jumps in height and surfactant concentration gradient the various waves and combinations are strikingly different from what is observed in the case of flow on a horizontal plane jump conditions admit new shock waves sustained by a linear surfactant wave traveling upstream the stability of these waves is investigated analytically and numerically for initial value problems a critical ratio of upstream to downstream height separates two distinct long time wave patterns below the critical ratio there is also an exact solution in which the height is piecewise constant and

linear resolution for consequence finding abstract in this paper we re evaluate the consequence finding problem within first order logic firstly consequence finding is generalized to the problem in which only interesting clauses having a certain property called characteristic clauses should be found the use of characteristic clauses enables characterization of various reasoning problems of interest to ai including abduction nonmonotonic reasoning prime implicates and truth maintenance systems secondly an extension of the model elimination theorem proving procedure sol resolution is presented providing an effective mechanism complete for finding the characteristic clauses an important feature of sol resolution is that it constructs such a subset of consequences directly without testing each generated clause for the required property we also discuss efficient but incomplete variations of sol resolution and their properties which address finding the most specific and the least specific abductive explanations

the satisfiability problem for a class consisting of horn sentences and some non horn sentences in porportional logic in this paper the satisfiability problem for a class of proportional sentences is considered here a sentence is a set of clauses a clause is a set of literals first it is proposed that a class s 0 of propositional sentences which properly includes the class of propositional horn sentences a sentence c 1 c n is in s 0 if there are sets p 1 p n of positive literals such that 1 p 1 p 2 p n 2 p i c i for 1 i n and 3 c i p i is a horn clause for 1 i n then it is proposed that a new inference rule based on the resolution principle by which un satisfiability for s 0 in polynomial time can be decided

first order lub approximations characterization and algorithms one of the major approaches to approximation of logical theories is the upper and lower bounds approach introduced by selman and kautz 1991 1996 in this paper we address the problem of lowest upper bound lub approximation in a general setting we characterize lub approximations for arbitrary target languages both propositional and first order and describe algorithms of varying generality and efficiency for all target languages proving their correctness we also examine some aspects of the computational complexity of the algorithms both propositional and first order show that they can be used to characterize properties of whole families of resolution procedures discuss the quality of approximations and relate lub approximations to other approaches existing in the literature which are not typically seen in the approximation framework and which go beyond the knowledge compilation perspective that led to the introduction of lubs

horn approximations of empirical data abstract formal ai systems traditionally represent knowledge using logical formulas sometimes however a model based representation is more compact and enables faster reasoning than the corresponding formula based representation the central idea behind our work is to represent a large set of models by a subset of characteristic models more specifically we examine model based representations of horn theories and show that there are large horn theories that can be exactly represented by an exponentially smaller set of characteristic models we show that deduction based on a set of characteristic models requires only polynomial time as it does using horn theories more surprisingly abduction can be performed in polynomial time using a set of characteristic models whereas abduction using horn theories is np complete finally we discuss algorithms for generating efficient representations of the horn theory that best approximates a general set of models

existence and multiplicity results for nonlinear boundary value problems this paper studies the existence of positive solutions for a class of boundary value problems of elliptic degenerate equations by using bifurcation and fixed point index theories in the frame of approximation arguments the criteria of the existence multiplicity and nonexistence of positive solutions are established

an algorithm to compute circumscription abstract mccarthy s theory of circumscription appears to be the most powerful among various formalizations of nonmonotonic reasoning designed to handle incomplete and negative information in knowledge representation systems in this paper we describe a query answering algorithm for circumscriptive theories the closed world assumption cwa and its generalizations the generalized closed world assumption gcwa and the extended closed world assumption ecwa can be considered as special forms of circumscription consequently our algorithm also applies to answering queries in theories using the closed world assumption and its generalizations similarly since prioritized circumscription is equivalent to a conjunction of parallel circumscriptions our algorithm can be used to answer queries in theories circumscribed by prioritized circumscription

positive radial symmetric solutions to an exterior elliptic robin boundary value problem and application abstract we study the existence uniqueness and behavior of positive radial symmetric solutions of the exterior boundary value problem u h x f u in r n b 0 r 0 u n a u on and u x 0 as x when a 0 the robin boundary condition has a wrong sign and this makes the analysis of the problem interesting and non trivial we determine a sharp condition on the coefficient a for the existence of positive spherically symmetric solutions of the boundary value problem the important model case f u u 1 7 a 1 2 r 0 and 1 2 r 0 is related to the initial data problem in general relativity for this model case as an example of application of our results we obtain the existence and uniqueness of the conformal factor corresponding to the hamiltonian constraint equation in the case of a single black hole in the radial symmetric regime