infinitely many non negative solutions for a dirichlet problem involving p x laplacian abstract in this paper we consider a dirichlet problem involving the p x laplacian of the type div u p x 2 u f x u in u 0 on we prove the existence of infinitely many non negative solutions of the problem by applying a general variational principle due to b ricceri and the theory of the variable exponent sobolev spaces

objective analyses and mapping techniques for rainfall fields an objective comparison many methods have been proposed and applied individually to rainfall fields in order to estimate point or average values at ungauged sites this paper reviews some of the usual as well as some of the more recent techniques they are classified according to their fundamental principles optimality criteria and practical aspects some theoretical developments mostly for the statistically based techniques are offered and the practical aspects are mainly directed to the particular case of rainfall fields a case study is presented for a region with particularly high rainfall variability providing a good sample of events for testing the sensitivity of the estimation to the different methods used the identification of statistical structure functions required by certain methods using regionalized variable concepts is discussed in detail for the case considered method evaluation is based on a classical validation technique that divides the available stations into two separate networks i e a base network is used to perform estimations at the stations of a test network for a set of independent storm events careful attention is paid to result interpretation and visualisation finally conclusions are drawn as to which method should be implemented taking into account cost efficiency considerations

infinitely many solutions for a differential inclusion problem in r n abstract in this paper we consider the differential inclusion problem di p u u p 2 u x f u x x r n u w 1 p r n where 2 n p l 1 r n l r n is radially symmetric and f stands for the generalized gradient of a locally lipschitz function f r r under suitable oscillatory assumptions on the potential f at zero or at infinity we show the existence of infinitely many radially symmetric solutions of di no symmetry requirement on f is needed our approach is based on a non smooth ricceri type variational principle developed by marano and motreanu j differential equations 182 2002 108 120

existence of infinitely many solutions for a neumann problem involving the p x laplacian abstract in this paper we consider the neumann problem involving the p x laplacian of the type div u p x 2 u x u p x 2 u f x u g x u in u 0 on we prove the existence of infinitely many solutions of the problem under weaker hypotheses by applying a variational principle due to b ricceri and the theory of the variable exponent sobolev spaces our results are an improvement and generalization of the relative results obtained by b ricceri for the p laplacian case

a critical point theorem and existence results for a nonlinear boundary value problem in this paper the existence of non zero solutions to a neumann boundary value problem is established multiplicity results are also pointed out the approach is based on a novel critical point theorem

assessing the uncertainty associated with intermittent rainfall fields 1 in many practical situations where spatial rainfall estimates are needed rainfall occurs as a spatially intermittent phenomenon an efficient geostatistical method for rainfall estimation in the case of intermittency has previously been published and comprises the estimation of two independent components a binary random function for modeling the intermittency and a continuous random function that models the rainfall inside the rainy areas the final rainfall estimates are obtained as the product of the estimates of these two random functions however the published approach does not contain a method for estimation of uncertainties the contribution of this paper is the presentation of the indicator maximum likelihood estimator from which the local conditional distribution of the rainfall value at any location may be derived using an ensemble approach from the conditional distribution representations of uncertainty such as the estimation variance and confidence intervals can be obtained an approximation to the variance can be calculated more simply by assuming rainfall intensity is independent of location within the rainy area the methodology has been validated using simulated and real rainfall data sets the results of these case studies show good agreement between predicted uncertainties and measured errors obtained from the validation data

improving dynamic programming to solve image registration a new method of dynamic programming dp is presented a picture is paired with a reference map in order to arrive at picture registration an ordered sequence of primitive patterns is formed from the map an attempt is made to locate a similar sequence from the picture using classical picture processing methods this yields a distorted and unordered sequence marked by noise dp is then used to search for a common match to the two sequences both the initial and final registration states are however unknown moreover the continuity of the path is frequently interrupted due to shortcomings in detection or perhaps occlusions thus classical dp algorithms appear to give only poor results under practical conditions when well adapted to treat signals issued from a first order markovian process they can be used as this method shows to treat kth order processes the concept of the virtual state kept in memory suspends broken paths until they can be reconnected thus bridging the existing gaps between the different parts of the path the proposed algorithm has been applied to satellite images with their contours sectioned by clouds the result leads to the guarantee of very good registration in spite of image contours badly hampered by noise and or clouds

remarks on ricceri s variational principle and applications to the p x laplacian equations abstract in this paper we give some remarks on a variational principle of ricceri in the case of sequentially weakly lower semi continuous functionals defined on a reflexive real banach space in particular we introduce the notions of ricceri block and ricceri box which are more convenient in some applications than the weakly connected components using the variational principle of ricceri and a local mountain pass lemma we study the multiplicity of solutions of the p x laplacian equations with neumann dirichlet or no flux boundary condition and under appropriate hypotheses in which the integral functionals need not satisfy the ps condition on the global space we prove that the problem has at least seven solutions

infinitely many solutions for a class of discrete non linear boundary value problems the existence of infinitely many solutions for a discrete non linear dirichlet problem involving the p laplacian under appropriate oscillating behaviours of the non linear term is established the approach is based on the critical point theory

statistical estimation of polynomial generalized covariance functions and hydrologic applications minimum variance unbiased linear estimation theory has found many applications in the analysis of spatial rainfall and hydrogeologic data estimation of point values or areal averages calculation of variances of estimation error and network design however the important problem of inferring the spatial structure or interdependence of the function of interest has received relatively less attention three methods for the estimation of the parameters of matheron s polynomial generalized covariance function a useful model for nonstationary functions are presented and evaluated maximum likelihood ml minimum variance unbiased quadratic mvuq and minimum norm least squares the estimation error covariance matrix of the parameters is calculated with each of these methods ml and mvuq estimation have very good properties and for reasonably large samples give very similar results minimum norm estimation is appropriate for preliminary data analysis the application of these methodologies is illustrated with a set of rainfall data and problems of implementation are discussed it is shown that the estimation of the parameters of the covariance function involves sizeable errors it is suggested that in practice it may be rather difficult to identify the parameters of all but simple models it is important that future research evaluate the effects of parameter uncertainty in the circulation of estimation error variances of point or areal averages and in the design of hydrologic data collection networks

perturbed kirchhoff type neumann problems in orlicz sobolev spaces the aim of this paper is to establish the existence of infinitely many solutions for perturbed kirchhoff type non homogeneous neumann problems involving two parameters to be precise we prove that an appropriate oscillating behaviour of the nonlinear term even under small perturbations ensures the existence of infinitely many solutions our approach is based on recent variational methods for smooth functionals defined on orlicz sobolev spaces

space time simulation of intermittent rainfall with prescribed advection field adaptation of the turning band method 1 space time rainfall simulation is useful to study questions like for instance the propagation of rainfall measurement uncertainty in hydrological modeling this study adapts a classical gaussian field simulation technique the turning band method in order to produce sequences of rainfall fields satisfying three key features of actual precipitation systems i the skewed point distribution and the space time structure of nonzero rainfall nzr ii the average probability and the space time structure of intermittency and iii a prescribed advection field the acronym of our simulator is sampo for simulation of advected mesoscale precipitations and their occurrence sampo assembles various theoretical developments available from the literature the concept of backtrajectories introduces a priori any type of advection field in the heart of the turning band method tbm tbm outputs transformation into rainfall fields with a desired structure is controlled using chebyshev hermite polynomial expansion the intermittency taken as a binary process statistically independent of the nzr process allows the use of a common algorithm for both processes the 3 d simulation with a space time anisotropy captures important details of the precipitation kinematics summarized by the taylor velocity of both nzr and intermittency a case study based on high resolution weather radar data serves as an example of model inference illustrative simulations revisit some classical questions about rainfall variography like the influence of advection or intermittency they also show the combined role of taylor s and advection velocities

on the nonlinear schrodinger equation on the poincare ball model abstract in this paper we prove the existence of a sequence of nonnegative weak solutions for the following problem h u u f u in b n u h 1 2 b n where h denotes the laplace beltrami operator on the poincare ball model b n with n 3 of the hyperbolic space h n l 1 b n l b n is a nonnegative and not identically zero radially symmetric potential f is a suitable continuous function and is a positive real parameter the analysis developed in this paper combines a compactness embedding result due to skrzypczak and tintarev 2013 theorem 1 3 and proposition 3 1 some group theoretical arguments on the poincare ball model b n and variational methods for smooth functionals defined on the sobolev space h 1 2 b n associated to the homogeneous hadamard manifold b n

infinitely many solutions for a dirichlet problem involving the p laplacian the existence of infinitely many solutions for an autonomous elliptic dirichlet problem involving the p laplacian is investigated the approach is based on variational methods

a neumann boundary value problem for the sturm liouville equation abstract in this paper we prove the existence of infinitely many solutions to a neumann boundary value problem for the sturm liouville equation results of the existence of three solutions are also established the approach is based on multiple critical points theorems

a robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry abstract this paper proposes a robust approach to image matching by exploiting the only available geometric constraint namely the epipolar constraint the images are uncalibrated namely the motion between them and the camera parameters are not known thus the images can be taken by different cameras or a single camera at different time instants if we make an exhaustive search for the epipolar geometry the complexity is prohibitively high the idea underlying our approach is to use classical techniques correlation and relaxation methods in our particular implementation to find an initial set of matches and then use a robust technique the least median of squares lmeds to discard false matches in this set the epipolar geometry can then be accurately estimated using a meaningful image criterion more matches are eventually found as in stereo matching by using the recovered epipolar geometry a large number of experiments have been carried out and very good results have been obtained regarding the relaxation technique we define a new measure of matching support which allows a higher tolerance to deformation with respect to rigid transformations in the image plane and a smaller contribution for distant matches than for nearby ones a new strategy for updating matches is developed which only selects those matches having both high matching support and low matching ambiguity the update strategy is different from the classical winner take all which is easily stuck at a local minimum and also from loser take nothing which is usually very slow the proposed algorithm has been widely tested and works remarkably well in a scene with many repetitive patterns

existence results for dynamic sturm liouville boundary value problems via variational methods abstract several conditions ensuring existence of solutions of a dynamic sturm liouville boundary value problem are derived variational methods are utilized in the proofs an example illustrating the main results is given

a critical points approach for the existence of multiple solutions of a dirichlet quasilinear system abstract in this paper we establish the existence of at least three classical solutions for the dirichlet quasilinear elliptic system p i 1 u i x p i 2 u i x f u i x u 1 u n g u i x u 1 u n h i x u i x a b u i a u i b 0 for i 1 n our main tool is a recent three critical points theorem of b ricceri a three critical points theorem revisited nonlinear anal 70 2009 3084 3089

existence and multiplicity of solutions for fourth order boundary value problems with parameters abstract in this paper we study the existence and multiplicity of the solutions for the fourth order boundary value problem bvp u 4 t u t u t f t u t 0 t 1 u 0 u 1 u 0 u 1 0 where f 0 1 r r is continuous r and r are parameters by means of the idea of the decomposition of operators shown by chen w y chen a decomposition problem for operators xuebao of dongbei renmin university 1 1957 95 98 see also m krasnosel skii topological methods in the theory of nonlinear integral equations gostehizdat moscow 1956 and the critical point theory we obtain that if the pair is on the curve 2 4 satisfying 2 2 then the above bvp has at least one two three and infinitely many solutions for being in different interval respectively

invariant representation matching and pose estimation of 3d space curves under similarity transformations this paper presents a system for matching and pose estimation of 3d space curves under the similarity transformation composed of rotation translation and uniform scaling the system makes use of constraints not only on the feature points but also on curve segments a representation called the similarity invariant coordinate system sics is presented for deriving semi local invariants of 3d curves the sics also enables an efficient exploration of constraints on the shape of the entire curve model based curve matching is performed in the principle of maximum a posteriori map probability in which markov random fields mrfs are used to model the prior probability results are given to demonstrate the matching with missing and extra feature points the extensive exploration of the curve shape constraints in both the matching and the pose estimation stages are shown to significantly improve the quality of the recognition and pose estimation

multiple constant sign and nodal solutions for nonlinear elliptic equations with the p laplacian we consider a nonlinear elliptic equation driven by the p laplacian with dirichlet boundary conditions using variational techniques combined with the method of upper lower solutions and suitable truncation arguments we establish the existence of at least five nontrivial solutions two positive two negative and a nodal sign changing solution our framework of analysis incorporates both coercive and p superlinear problems also the result on multiple constant sign solutions incorporates the case of concave convex nonlinearities

image registration by matching relational structures abstract we present a method of image registration where we use relational structures as representations of images and we register two images by finding a match between the two relational structures it is better than traditional cross correlation like techniques in several aspects it is insensitive to scaling rotation gray level modification and small relative motion between the two images the matching process makes use of star structures which have several advantages over conventional node structures

estimating motion and structure from correspondences of line segments between two perspective images presents an algorithm for determining 3d motion and structure from correspondences of line segments between two perspective images to the author s knowledge this paper is the first investigation of use of line segments in motion and structure from motion classical methods use their geometric abstraction namely straight lines but then three images are necessary for the motion and structure determination process in this paper the author shows that it is possible to recover motion from two views when using line segments the assumption used is that two matched line segments contain the projection of a common part of the corresponding line segment in space i e they overlap indeed this is what the author uses to match line segments between different views this assumption constrains the possible motion between two views to an open set in motion parameter space a heuristic consisting of maximizing the overlap leads to a unique solution both synthetic and real data have been used to test the proposed algorithm and excellent results have been obtained with real data containing a relatively large set of line segments

a general variational principle and some of its applications abstract in this paper given a reflexive real banach space x and two sequentially weakly lower semicontinuous functionals on x with strongly continuous and coercive we are mainly interested in the existence of infinitely many local minima of the functional for each sufficiently large r

on the relationship between two three critical point theorems abstract in this paper we analyze the hypotheses of two theorems which have proven to be useful tools for obtaining the existence of three critical points in nonlinear problems in both cases the hypotheses can be stated in terms of some elementary inequalities involving coercive in a suitable sense sets of affine functions we prove that the two resulting inequalities are in fact equivalent

multiple solutions for a coupled system of nonlinear fractional differential equations via variational methods in this paper a coupled system of nonlinear fractional differential equations is considered the existence of at least three distinct weak solutions is obtained by means of the variational methods and the critical point theory due to bonanno and marano in addition an example is presented to illustrate the feasibility and effectiveness of the main results

existence of three solutions for a non homogeneous neumann problem through orlicz sobolev spaces abstract the aim of this paper is to establish a multiplicity result for an eigenvalue non homogeneous neumann problem which involves a nonlinearity fulfilling a nonstandard growth condition precisely a recent critical points result for differentiable functionals is exploited in order to prove the existence of a determined open interval of positive eigenvalues for which the problem admits at least three weak solutions in an appropriate orlicz sobolev space

nonsmooth version of fountain theorem and its application to a dirichlet type differential inclusion problem abstract in this paper we establish a nonsmooth version of fountain theorem by adopting the framework of nonsmooth analysis theory which is a generalization of theorem 3 6 of willem 1996 2 then we present an application of this theorem to a dirichlet type differential inclusion problem

on the accuracy of areal rainfall estimation a case study the issue of the accuracy of areal rainfall estimation is discussed through a case study on a catchment area in the ckvennes region of france the basic tool for the analysis is a scaled estimation error variance which is computed from a scaled climatological variogram model of the rainfall field we show how this variance provides a theoretical criterion to compare the accuracy that can be expected with three linear estimators thiessen spline and kriging for various networks densities to support the methodology an experimental validation of the scald estimation error variance computation is per formed using reference areal rainfall values computed with a very high density network 5good estimates of mean areal rainfall are needed as inputs to hydrologic models when based on ground measurements their accuracy depends on the spatial variability of the rainfall process and on the rain gage networkdensity accuracy is of particular importance when areal rainfall estimates must be computed in real time as inputs to runoff forecasting models the high cost of equipping and maintaining the required telemetering facilities especially in mountainous regions often results in low density observation networks making the most of a given network whether telemetered or not is a prime concern shared by all operators and hydrologic designers consequently the interpolation of data collected from scattered rain gages has long been an important research topic in hydrology creutin and obled 1982 have compared the performances of commonly used linear estimators their study shows that for low to medium density networks sophisticated methods e g spline surface fitting or kriging give better results than simpler conventional methods e g thiessen polygons or arithmetic means furthermore various advantages and disadvantages are outlined for each method providing a basis for evaluating their applicability to specific hydrologic problems more recently a similar comparison was applied to annual rainfalls by tabios and salas 1985 yielding results consistent with those of creutin and obled however it is often more useful but also more difficult for a hydrologist to evaluate the error involved in areal rather than in point rainfall estimation the theoretical error variance of any linear areal rainfall estimator can obviously be computed under the assumption that the observations are a realization of a random field with a given covariance model however a major difficulty arises in validating the calculated theoretical variance from experimental data since no direct

infinitely many solutions for a class of dirichlet quasilinear elliptic systems abstract in this paper we prove the existence of infinitely many classical solutions for a class of dirichlet quasilinear elliptic systems the approach is based on variational methods

infinitely many solutions for the dirichlet problem involving the p laplacian abstract using a recent variational principle of ricceri we present a result of existence of infinitely many solutions for the dirichlet problem involving the p laplacian