fully nonlinear fourth order equations with functional boundary conditions abstract the aim of this paper consists in to give sufficient conditions to ensure the existence and location of the solutions of a nonlinear fully fourth order equation with functional boundary conditions the arguments make use of the upper and lower solutions method a laplacian operator and a fixed point theorem an application of the beam theory to a nonlinear continuous model of the human spine allows to estimate its deformation under some loading forces

there is no impact of exposure measurement error on latency estimation in linear models identification of the latency period for the effect of a time varying exposure is key when assessing many environmental nutritional and behavioral risk factors a pre specified exposure metric involving an unknown latency parameter is often used in the statistical model for the exposure disease relationship likelihood based methods have been developed to estimate this latency parameter for generalized linear models but do not exist for scenarios where the exposure is measured with error as is usually the case here we explore the performance of naive estimators for both the latency parameter and the regression coefficients which ignore exposure measurement error assuming a linear measurement error model we prove that in many scenarios under this general measurement error setting the least squares estimator for the latency parameter remains consistent while the regression coefficient estimates are inconsistent as has previously been found in standard measurement error models where the primary disease model does not involve a latency parameter conditions under which this result holds are generalized to a wide class of covariance structures and mean functions the findings are illustrated in a study of body mass index in relation to physical activity in the health professionals follow up study

remarks on j j nieto s paper nonlinear second order periodic boundary value problems and proved the following assertions suppose that f c 0 2n x r r is decreasing in u for each fixed t e 0 27r and that x p e c2 0 27r are lower and upper solutions for 1 then 1 if c d p on 0 2n then 1 admits a solution and the solution set of 1 in the sector a i is an rg 2 if c 2 i on 0 2rc then a 1 admits a solution b there exist positive constants sr s such that the solution set of 1 in the sector lx s fl s2 is an r the aim of this paper is to improve these assertions

boundary first order derivative estimates for fully nonlinear elliptic equations abstract in this paper we prove the estimates of modulus of continuity up to the boundary for the first order derivative of viscosity solutions for fully nonlinear uniformly elliptic equations under dini boundary data with the domain in the same class as a corollary we derive c 1 boundary regularity

boundary pointwise c1 α and c2 α regularity for fully nonlinear elliptic equations abstract in this paper we obtain the boundary pointwise c 1 and c 2 regularity for viscosity solutions of fully nonlinear elliptic equations that is if is c 1 or c 2 at x 0 the solution is c 1 or c 2 at x 0 our results are new even for the laplace equation moreover our proofs are simple

second order periodic boundary value problems on time scales in this paper we study the existence of solutions of periodic boundary value problem for second order nonlinear dynamic equations on time scales for this purpose we use two methods here first sign properties of the green s function are investigated and existence results of bounded solutions of nonlinear boundary value problems are established as a result of schauder fixed point theorem second the monotone method is discussed to assure the existence and uniqueness of solutions of such periodic boundary value problems on time scales

elliptic equations on convex domains with nonhomogeneous dirichlet boundary conditions abstract in this paper we will study the differentiability on the boundary of solutions of elliptic non divergence differential equations on convex domains the results are divided into two cases i at the boundary points where the blow up of the domain is not the half space if the boundary function is differentiable then the solution is differentiable ii at the boundary points where the blow up of the domain is the half space the differentiability of the solution needs an extra dini condition for the boundary function counterexample is given to show that our results are optimal

solvability of three point boundary value problems for second order differential equations with deviating arguments the monotone iterative technique is used to boundary problems for second order ordinary differential equations with deviating arguments corresponding results are formulated when the problem has extremal solutions or weakly coupled extremal quasi solutions

quasi solutions for generalized second order differential equations with deviating arguments this paper deal with boundary value problems for generalized second order differential equations with deviating arguments existence of quasi solutions and solutions are proved by monotone iterative method examples with numerical results are added

differentiability at lateral boundary for fully nonlinear parabolic equations abstract for fully nonlinear uniformly parabolic equations the first derivatives regularity of viscosity solutions at lateral boundary is studied under new dini type conditions for the boundary which is called reifenberg dini conditions and is weaker than usual dini conditions

multi point boundary value problems for second order functional differential equations this paper is concerned with the existence of extreme solutions of multi point boundary value problem for a class of second order functional differential equations we introduce a new concept of lower and upper solutions by using the method of upper and lower solutions and monotone iterative technique we obtain the existence of extreme solutions

nonlinear second order periodic boundary value problems abstract in this paper we study a periodic boundary value problem pbvp for brevity of second order it is well known that if and are upper and lower solutions respectively with then there exists a solution u such that u when nothing was known the main purpose of this paper is to consider this last case also we study the structure of the set of solutions of the pbvp in the sector when and we apply the results to the case

a monotone method for constructing extremal solutions to second order periodic boundary value problems abstract in this paper we describe a constructive method which yields two monotone sequences that converge uniformly to extremal solutions to the periodic boundary value problem u t f t u u t t 0 2 u 0 u 2 u 0 u 2 in the presence of an upper solution and a lower solution with

correction of logistic regression relative risk estimates and confidence intervals for systematic within person measurement error errors in the measurement of exposure that are independent of disease status tend to bias relative risk estimates and other measures of effect in epidemiologic studies toward the null value two methods are provided to correct relative risk estimates obtained from logistic regression models for measurement errors in continuous exposures within cohort studies that may be due to either random unbiased within person variation or to systematic errors for individual subjects these methods require a separate validation study to estimate the regression coefficient lambda relating the surrogate measure to true exposure in the linear approximation method the true logistic regression coefficient beta is estimated by beta lambda where beta is the observed logistic regression coefficient based on the surrogate measure in the likelihood approximation method a second order taylor series expansion is used to approximate the logistic function enabling closed form likelihood estimation of beta confidence intervals for the corrected relative risks are provided that include a component representing error in the estimation of lambda based on simulation studies both methods perform well for true odds ratios up to 3 0 for higher odds ratios the likelihood approximation method was superior with respect to both bias and coverage probability an example is provided based on data from a prospective study of dietary fat intake and risk of breast cancer and a validation study of the questionnaire used to assess dietary fat intake

a generalization of the monotone iterative technique for nonlinear second order periodic boundary value problems abstract the purpose of this paper is to study a periodic boundary value problem for a nonlinear ordinary differential equation of second order we generalize the monotone iterative method to cover some new situations and present a new approach considering the monotone iterates as orbits of a discrete dynamical system

survival analysis with error prone time varying covariates a risk set calibration approach occupational environmental and nutritional epidemiologists are often interested in estimating the prospective effect of time varying exposure variables such as cumulative exposure or cumulative updated average exposure in relation to chronic disease endpoints such as cancer incidence and mortality from exposure validation studies it is apparent that many of the variables of interest are measured with moderate to substantial error although the ordinary regression calibration approach is approximately valid and efficient for measurement error correction of relative risk estimates from the cox model with time independent point exposures when the disease is rare it is not adaptable for use with time varying exposures by re calibrating the measurement error model within each risk set a risk set regression calibration method is proposed for this setting an algorithm for a bias corrected point estimate of the relative risk using an rrc approach is presented followed by the derivation of an estimate of its variance resulting in a sandwich estimator emphasis is on methods applicable to the main study external validation study design which arises in important applications simulation studies under several assumptions about the error model were carried out which demonstrated the validity and efficiency of the method in finite samples the method was applied to a study of diet and cancer from harvard s health professionals follow up study hpfs

extremal solutions of second order nonlinear periodic boundary value problems we study a periodic boundary value problem for a nonlinear ordinary differential equation of second order when the nonlinearity is given by a caratheodory function we generalize the monotone iterative method to cover the fully nonlinear case

a monotone method for constructing extremal solutions of second order scalar boundary value problems a monotone iterative method is given for the construction of extremal solutions to second order scalar boundary value problems starting from a pair of upper and lower solutions the fully nonlinear case is considered

anti periodic boundary value problems of second order impulsive differential equations this paper discusses anti periodic boundary value problems of second order impulsive differential equations by using the method of upper and lower solutions coupled with the monotone iterative technique new existence results of coupled solutions and uniqueness of problems are obtained

nonlinear boundary value problems for second order differential equations with causal operators in this paper we deal with second order differential equations with causal operators to obtain sufficient conditions for existence of solutions we use a monotone iterative method we investigate both differential equations and differential inequalities an example illustrates the results obtained

periodic boundary value problems for nonlinear higher order ordinary differential equations we study a class of boundary value problems for linear and nonlinear ordinary differential equations of higher order we study the solution set and present a maximum principle as a consequence we show the validity of the monotone method and obtain the extremal solutions between the upper and lower solutions

periodic boundary value problems of second order impulsive differential equations abstract this paper discusses periodic boundary value problems of second order impulsive differential equations by using schaeffer s fixed point theorem and monotone iterative technique some existence results are obtained

on the regularity theory of fully nonlinear parabolic equations ii recently m crandall and p l lions 3 developed a very successful method for proving the existence of solutions of nonlinear second order partial differential equations their method called the theory of viscosity solutions also applies to fully nonlinear equations in which even the second order derivatives can enter in nonlinear fashion solutions produced by the viscosity method are guaranteed to be continuous but not necessarily smooth here we announce smoothness results for viscosity solutions our methods extend those of 1 we obtain krylov safonov i e c estimates 8 c 1 schauder c and w estimates for viscosity solutions of uniformly parabolic equations in general form the results can be viewed as a priori estimates on the classical c solutions our method produces in particular regularity results for a broad new array of nonlinear heat equations including the bellman equation 6

interior a priori estimates for solutions of fully non linear equations on etend une theorie de perturbations aux solutions d equations uniformement elliptiques d ordre 2 totalement non lineaires

positive solutions of periodic boundary value problems for impulsive differential equations in this paper we discuss the existence of positive solutions of periodic boundary value problems for second order impulsive equations the existence and multiplicity of positive solutions are established and the proof is based upon fixed point theorems in cone

corrections for exposure measurement error in logistic regression models with an application to nutritional data two correction methods are considered for multiple logistic regression models with some covariates measured with error both methods are based on approximating the complicated regression model between the response and the observed covariates with simpler models the first model is the logistic approximation proposed by rosner et al and the second is a second order extension of this model only the mean and covariance matrix of the true values of the covariates given the observed values have to be specified but no distributional assumptions about the measurement error are made the parameters related to the conditional moments are estimated from a separate validation data set the correction methods considered here are compared to other methods proposed in the literature they are also applied to a multiple logistic model describing the effect of nutrient intakes on the ratio of serum hdl cholesterol to total cholesterol the data constitute baseline data from an epidemiological cohort study in which a separate pilot study has been carried out to obtain validation information in the example the corrected parameter estimates from the two approximate models are very similar both differ considerably from the naive logistic estimates indicating a large effect of the measurement error the various assumptions required by the correction methods are also discussed

the method of lower and upper solutions for second third fourth and higher order boundary value problems abstract in this paper we develop the monotone method in the presence of lower and upper solutions for the problem u n t t u t u i a u i b i r i 0 n 1 where is a caratheodory function we obtain necessary and sufficient conditions in to guarantee the existence of solutions between a lower solution and an upper solution for n 2 if n 3 either or and n 4 if furthermore we obtain sufficient conditions in for n 2 k 6 when