existence and uniqueness of positive solutions for fourth order nonlinear singular continuous and discrete boundary value problems using the mixed monotone method we establish the existence and uniqueness of positive solutions for some fourth order nonlinear singular continuous and discrete boundary value problem the theorems obtained are very general and complement previously known results

positive solutions of fourth order multi point boundary value problems with bending term abstract in this paper we study m point boundary value problem for fourth order ordinary differential equation with bending term x x 4 t g t f t x t x t t 0 1 x 0 0 x 1 i 1 m 2 a i x i x 0 0 x 1 i 1 m 2 b i x i where 0 0 1 2 m 2 m 1 1 by constructing an available integral operator and combining fixed point index theorem we establish sufficient conditions for the existence of positive solutions under some conditions concerning the first eigenvalue corresponding to the relevant linear operator the interesting point of the results is that the nonlinear term g may be singular at t 0 and or t 1 moreover f t u v is also allowed to have singularity at u 0 and or v 0

existence of a positive solution of a fourth order boundary value problem abstract in this paper the existence of a positive solution of the boundary value problem of the following fourth order nonlinear differential equation x 4 f t x x x 0 x 0 x t x t 0 is discussed

a parametric ribcage geometry model accounting for variations among the adult population the objective of this study is to develop a parametric ribcage model that can account for morphological variations among the adult population ribcage geometries including 12 pair of ribs sternum and thoracic spine were collected from ct scans of 101 adult subjects through image segmentation landmark identification 1016 for each subject symmetry adjustment and template mesh mapping 26 180 elements for each subject generalized procrustes analysis gpa principal component analysis pca and regression analysis were used to develop a parametric ribcage model which can predict nodal locations of the template mesh according to age sex height and body mass index bmi two regression models a quadratic model for estimating the ribcage size and a linear model for estimating the ribcage shape were developed the results showed that the ribcage size was dominated by the height p 0 000 and age sex interaction p 0 007 and the ribcage shape was significantly affected by the age p 0 0005 sex p 0 0002 height p 0 0064 and bmi p 0 0000 along with proper assignment of cortical bone thickness material properties and failure properties this parametric ribcage model can directly serve as the mesh of finite element ribcage models for quantifying effects of human characteristics on thoracic injury risks

a generalized multi point boundary value problem for second order ordinary differential equations let f 0 1 x r 2 r be a function satisfying caratheodory s conditions and e t l 1 0 1 let x i t j 0 1 a i b j r i 1 2 m 2 j 1 2 n 2 0 x 1 x 2 x m 2 1 0 t 1 t 2 t n 2 1 be given this paper is concerned with the problem of existence of a solution for the generalized multi point boundary value problems x t f t x t x t e t 0

on positive solutions for fourth order boundary value problem with impulse in this paper we consider a fourth order boundary value problem with impulse first we establish criteria for the existence of one or more than one positive solution of a non eigenvalue problem second we are concerned with determining values of l for which there exist positive solutions for an eigenvalue problem in both problems we shall use the krasnoselskii fixed point theorem

eigenvalues of fourth order singular sturm liouville boundary value problems abstract in this paper by establishing a new comparison theorem and constructing upper and lower solutions some sufficient conditions of existence of positive solutions for the following nonlinear fourth order singular sturm liouville eigenvalue problem 1 p t p t u t f t u t 0 1 u 0 u 1 0 u 0 lim t 0 p t u t 0 u 1 lim t 1 p t u t 0 are established due to the schauder s fixed point theorem for large enough where 0 0 f and p can be singular at t 0 and or 1 moreover f can also be singular at u 0 in addition some peculiar cases are discussed and some further results are obtained

solvability of a three point nonlinear boundary value problem for a second order ordinary differential equation in case f x u u ps x p x u pjx u with pk 0 l 4 r locally integrable the boundary value problem l lt 1 2 was studied by kiguradze and lomtatidze i the purpose of this paper is to obtain existence and uniqueness theorems for the boundary value problem 1 1 t 1 2 under natural conditions on f using degree theoretic arguments we note that if u is a solution of 1 1 1 2 then there exists at least one 5 e q l such that u c 0 accordingly the boundary value problem

existence and multiplicity of solutions of a kind of fourth order boundary value problem abstract in this paper the existence and multiplicity results of the solutions are obtained for the fourth order boundary value problem u 4 t f t u t for all t 0 1 subject to u 0 u 1 u 0 u 1 0 where f is continuous the monotone operator theory and critical point theory are employed to discuss this problem respectively

the hausdorff dimension of the level sets of takagi s function abstract recently maddock 2006 12 has conjectured that the hausdorff dimension of each level set of takagi s function is at most 1 2 we prove this conjecture using the self affinity of the function of takagi and the existing relationship between the hausdorff and box counting dimensions

multiple solutions for fourth order boundary value problem abstract in this paper we study the existence and multiplicity of nontrivial solutions for the fourth order two point boundary value problems making use of the theory of fixed point index in cone and leray schauder degree under general conditions on nonlinearity we prove that there exist at least six different nontrivial solutions for the fourth order two point boundary value problems furthermore if the nonlinearity is odd we obtain that there exist at least eight different nontrivial solutions

positive solutions of the nonlinear fourth order beam equation with three parameters abstract this paper is concerned with the existence and nonexistence of positive solutions of the nonlinear fourth order beam equation 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 t u 0 1 0 0 is continuous and and are parameters we show that there exists a 0 such that the above boundary value problem bvp has at least two one and no positive solutions for 0 and respectively furthermore by using the semiorder method on cones of banach space we establish a uniqueness criterion for positive solution of the bvp in particular such a positive solution u t of the bvp depends continuously on the parameter i e u t is nondecreasing in lim 0 u t 0 and lim u t for any t 0 1

multiplicity results for positive solutions of some semi positone three point boundary value problems in this paper some multiplicity results for positive solutions of some singular semi positone three point boundary value problem be obtained by using the fixed point index method

positive solutions of fourth order boundary value problems with two parameters abstract in this paper the existence results of positive solutions are obtained for fourth order boundary value problem u 4 u u f t u 0 where f 0 1 r r is continuous r and satisfy

positive solutions for a higher order four point boundary value problem with a p laplacian in this paper we study the existence of positive solutions of the following nth order four point boundary value problem with one dimensional p laplacian f p u n 1 h t f t u t u t u n 2 t 0 0 3 u i 0 0 0 i n 3 u n 1 0 au n 2 x 0 n 3 u n 1 1 bu n 2 h 0 n 3 where f p s s p 2s p 1 0 a 1 x 0 b 11 h 0 x h 1 by using a fixed point theorem in cones the existence of a positive solution and multiple positive solutions is obtained also at the end of this paper we present a generalization of this problem

necessary and sufficient conditions for the existence of quasi symmetric positive solutions of singular boundary value problem abstract this paper investigates the existence of quasi symmetric positive solutions for fourth order singular three point boundary value problem we first give definitions of quasi symmetric lower and upper solutions by constructing quasi symmetric lower and upper solutions and using the schauder fixed point theorem necessary and sufficient conditions for existence results are obtained

the existence and the uniqueness of symmetric positive solutions for a fourth order boundary value problem the purpose of this paper is to investigate the existence and the uniqueness of symmetric positive solutions for a class of fourth order boundary value problem y 4 t f t y t t 0 1 y 0 y 1 y 0 y 1 0 by using the fixed point index method we establish the existence of at least one or at least two symmetric positive solutions for the above boundary value problem further by using a fixed point theorem of general a concave operators we also present criteria which guarantee the existence and uniqueness of symmetric positive solutions for the above boundary value problem

symmetric positive solutions for p laplacian fourth order differential equations with integral boundary conditions this paper investigates the existence and multiplicity of symmetric positive solutions for a class of p laplacian fourth order differential equations with integral boundary conditions the arguments are based upon a specially constructed cone and the fixed point theory for cones the nonexistence of a positive solution is also studied

symmetric positive solutions for nonlocal boundary value problems of fourth order abstract the singular fourth order nonlocal boundary value problem u t h t f t u 0 t 1 u 0 u 1 0 1 p s u s d s u 0 u 1 0 1 q s u s d s is considered under some suitable conditions concerning the first eigenvalue of the corresponding linear operator where p q l 1 0 1 h 0 1 0 is continuous symmetric on 0 1 and may be singular at t 0 and t 1 f 0 1 0 0 is continuous and f x is symmetric on 0 1 for all x 0 the existence of at least one symmetric positive solution is obtained by the application of the fixed point index in cones

upper and lower solution method for fourth order four point boundary value problems this paper is concerned with the fourth order ordinary differential equation u 4 t f t u t u t 0 0 some new existence results are obtained by developing the upper and lower solution method and the monotone iterative technique

the upper and lower solution method for a class of singular nonlinear second order three point boundary value problems in this paper we develop the upper and lower solution method and the monotone iterative technique for a class of singular nonlinear second order three point boundary value problems a maximum principle is established and some new existence results are obtained

positive solutions of some nonlocal fourth order boundary value problem by the use of the krasnosel skii s fixed point theorem the existence of one or two positive solutions for the nonlocal fourth order boundary value problemu 4 t email protected t email protected t u t u t 00 email protected c 0 1 x 0 x 0 0

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

positive solutions for fourth order differential equations with deviating arguments and integral boundary conditions abstract in this paper we investigate integral boundary value problems for fourth order differential equations with deviating arguments we discuss our problem both for advanced or delayed arguments we establish sufficient conditions under which such problems have positive solutions to obtain the existence of multiple at least three positive solutions we use a fixed point theorem due to avery and peterson an example is also included to illustrate that corresponding assumptions are satisfied the results are new

on the level sets of the takagi van der waerden functions abstract this paper examines the level sets of the continuous but nowhere differentiable functions f r x n 0 r n r n x where x is the distance from x to the nearest integer and r is an integer with r 2 it is shown by using properties of a symmetric correlated random walk that almost all level sets of f r are finite with respect to lebesgue measure on the range of f but that for an abscissa x chosen at random from 0 1 the level set at level y f r x is uncountable almost surely as a result the occupation measure of f r is singular

infinite derivatives of the takagi van der waerden functions abstract in this paper we characterize the set of points where the lateral derivatives of the takagi van der waerden functions are infinite we also prove that the set of points with infinite derivative has hausdorff dimension one and lebesgue measure zero

positive solutions of fourth order four point boundary value problems with p laplacian operator in this paper we consider the existence of positive solutions for the singular fourth order p laplacian equation p u t f t u t 0 t 1 with the four point boundary conditions u 0 0 u 1 au u 0 0 u 1 bu where p t t p 2t p 1 0 1 f c 0 1 0 0 may be singular at t 0 and or 1 and u 0 by using the upper and lower solution method and fixed point theorems the existence of positive solutions to the above the boundary value problem is obtained

symmetric positive solutions of boundary value problems with integral boundary conditions under conditions weaker than those used by ma we establish various results on the existence and nonexistence of symmetric positive solutions to fourth order boundary value problems with integral boundary conditions the arguments are based upon a specially constructed cone and the fixed point theory in a cone our results improve and extend that obtained in h ma symmetric positive solutions for nonlocal boundary value problems of fourth order nonlinear anal 68 2008 645 651 we illustrate our results by one example which cannot be handled using the existing results

positive solutions of nonlinear fourth order boundary value problems with local and non local boundary conditions we establish new existence results for multiple positive solutions of fourth order nonlinear equations which model deflections of an elastic beam we consider the widely studied boundary conditions corresponding to clamped and hinged ends and many non local boundary conditions with a unified approach our method is to show that each boundary value problem can be written as the same type of perturbed integral equation in the space c 0 1 involving a linear functional u but although we seek positive solutions the functional is not assumed to be positive for all positive u the results are new even for the classic boundary conditions of clamped or hinged ends when u 0 because we obtain sharp results for the existence of one positive solution for multiple solutions we seek optimal values of some of the constants that occur in the theory which allows us to impose weaker assumptions on the nonlinear term than in previous works our non local boundary conditions contain multi point problems as special cases and for the first time in fourth order problems we allow coefficients of both signs

existence of positive solutions for the nonlinear elastic beam equation via a mixed monotone operator abstract in this paper we use a mixed monotone operator method to investigate the existence and uniqueness of positive solution to a nonlinear fourth order boundary value problem which describes the deflection of an elastic beam with the left extreme fixed and the right extreme is attached to a bearing device given by a known function moreover we present a concrete example illustrating the result obtained

fourth order two point boundary value problems estimates by two sided bounds on presente une methode simple pour transformer des problemes aux deux points limites d ordre 4 en problemes d ordre 2

positive solutions for singular m point boundary value problems with positive parameter in this paper some new existence results for positive solutions for a class of singular m point boundary value problems with parameter be obtained

quantification of age related shape change of the human rib cage through geometric morphometrics abstract the aim of this study is to quantify patterns of age related shape change in the human thorax using procrustes superimposition landmarks n 106 selected from anonymized computed tomography ct scans of 63 adult males free of skeletal pathology were used to describe the form of the rib cage multivariate linear regression was used to determine a relationship between landmark location and age linear and quadratic models were also investigated a permutation test employing 1 105 random trials was used to assess the model significance for both model formulations linear relationships between the centroid size cs of a landmark set and the corresponding individual s height weight and bmi were conducted to enable scaling of the dimensionless results from the procrustes analysis a significance level of 0 05 was used for all tests the average age of the study subjects was 57 0 17 3 years complete landmark sets were obtained from most of the scans 44 of 63 the quadratic relationship between the age and landmark location was found to be significant p 0 037 thereby establishing a relationship between the age and thoracic shape change the linear relationship was mildly significant as well p 0 073 significant relationships between the centroid size of the dataset and subject weight height and bmi were determined with the best correlated value being weight p 0 002 r2 0 22 landmark datasets calculated using the quadratic model exhibited shape change consistent with the clinical observations increasing kyphosis and rounding of the thoracic cage procrustes superimposition represents a potential improvement in the approach used to generate computational models for injury biomechanics studies the coefficients from the quadratic model are provided and can be used to generate the complete set of model landmark data points at a given age

positive solutions for a class of boundary value problems with integral boundary conditions this paper investigates the existence and multiplicity of positive solutions for a class of nonlinear boundary value problems of fourth order differential equations with integral boundary conditions the arguments are based upon a specially constructed cone and the fixed point theory in cone the nonexistence of positive solutions is also studied

existence of a solution and a positive solution of a boundary value problem for a nonlinear fourth order dynamic equation abstract in this paper by using the schauder fixed point theorem we offer some existence criteria for a solution and a positive solution to the following fourth order two point boundary value problem on time scale t u t f t u t u t 0 t a 2 b u a a u 2 b b u a c u b d where a b t and a b

searching the least value method for solving fourth order nonlinear boundary value problems this paper obtains a searching least value slv method for a class of fourth order nonlinear boundary value problems is investigated the argument is based on the reproducing kernel space w 5 0 1 the approximate solutions u n x and u n k x are uniformly convergent to the exact solution u x and u k x k 1 2 3 4 respectively numerical results are verified that the method is quite accurate and efficient for this kind of problem

existence of positive solutions of a fourth order boundary value problem abstract we consider the fourth order boundary value problem u f t u u 0 t 1 u 0 u 1 u 0 u 1 0 where f t u p au b p u p near 0 0 and f t u p cu dp u p near we give conditions on the constants a b c d that guarantee the existence of positive solutions the proof of our main result is based upon global bifurcation techniques

upper and lower solution method for a fourth order four point boundary value problem on time scales in this work we consider a fourth order four point boundary value problem on time scales we establish criteria for the existence of a solution by developing the upper and lower solution method and the monotone iterative technique

multiple solutions of some boundary value problems with parameters abstract in this paper we study the existence and multiplicity of nontrivial solutions for the following second order dirichlet nonlinear boundary value problem with odd order derivative u t a u t b u t f t u t for all t 0 1 with u 0 u 1 0 where a b r 1 f c 1 0 1 r 1 r 1 by using the morse theory we impose certain conditions on f which are able to guarantee that the problem has at least one nontrivial solution two nontrivial solutions and infinitely many solutions separately

a statistical human rib cage geometry model accounting for variations by age sex stature and body mass index in this study we developed a statistical rib cage geometry model accounting for variations by age sex stature and body mass index bmi thorax ct scans were obtained from 89 subjects approximately evenly distributed among 8 age groups and both sexes threshold based ct image segmentation was performed to extract the rib geometries and a total of 464 landmarks on the left side of each subject s ribcage were collected to describe the size and shape of the rib cage as well as the cross sectional geometry of each rib principal component analysis and multivariate regression analysis were conducted to predict rib cage geometry as a function of age sex stature and bmi all of which showed strong effects on rib cage geometry except for bmi all parameters also showed significant effects on rib cross sectional area using a linear mixed model this statistical rib cage geometry model can serve as a geometric basis for developing a parametric human thorax finite element model for quantifying effects from different human attributes on thoracic injury risks

subject specific regression equations to estimate lower spinal loads during symmetric and asymmetric static lifting abstract workplace safety assessment personalized treatment design and back pain prevention programs require accurate subject specific estimation of spinal loads since no noninvasive method can directly estimate spinal loads easy to use regression equations that are constructed based on the results of complex musculoskeletal models appear as viable alternatives thus we aim to develop subject specific regression equations of l4 l5 and l5 s1 shear and compression forces during various symmetric asymmetric tasks using a nonlinear personalized finite element musculoskeletal trunk model kinematics and electromyography emg activities of 19 young healthy subjects were collected during 64 different symmetric asymmetric tasks to investigate the reliability and accuracy of the musculoskeletal model and regression equations we compared estimated trunk muscle activities and l4 l5 intradiscal pressures idps respectively with our own electromyography data emgs and reported in vivo pressure measurements although in general six independent rotation components three trunk t11 rotations and three pelvic s1 rotations are required to determine kinematics along the spine only two surrogate variables trunk flexion and its asymmetric angles satisfactorily predicted all six rotation components r2 0 94 regression equations developed based on subject specific inputs predicted spinal loads in satisfactory agreement with idp measurements r2 0 85 predicted muscle activities in the personalized musculoskeletal models were in moderate to weak agreements with our measured emgs in 19 participants based on dominance analysis trunk flexion and its asymmetry angle hand load weight hand load lever arm and body weight were the most important variables while the effects of body height and sex on spinal loads remained small

solvability of an m point boundary value problem for second order ordinary differential equations let 0 1 r2 r be a function satisfying caratheodory s conditions and e t l1 0 1 let i 0 1 ai r all of the ai s having the same sign i 1 2 m 2 0 1 2 m 2 1 be given this paper is concerned with the problem of existence of a solution for the m point boundary value problem x t t x t x t e t t 0 1 e formula conditions for the existence of a solution for the above boundary value problem are given using the leray schauder continuation theorem

existence of positive solutions of lidstone boundary value problems abstract we show that there exists at least one positive solution for lidstone boundary value problem 1 n u 2 n t f t u t u t u 2 n 1 t 0 t 1 u 2 i 0 u 2 i 1 0 i 0 1 n 1 under some suitable conditions our proof is based upon global bifurcation techniques

multiple positive solutions for a second order three point boundary value problem in this paper we study the second order three point boundary value problemu t a t u t b t u t h t f u 0 email protected 0 1 u 0 0 au h u 1 the existence criteria for multiple positive solutions is obtained by using krasnoselskii fixed point theorem and leggett williams fixed point theorem

existence and uniqueness of monotone positive solutions for an elastic beam equation with nonlinear boundary conditions this paper is concerned with the existence and uniqueness of monotone positive solutions for an elastic beam equation with nonlinear boundary conditions the proof of our main results is based upon a new fixed point theorem of generalized concave operators

positive solutions of fourth order nonlinear singular sturm liouville eigenvalue problems abstract we consider the existence of positive solutions for the following fourth order singular sturm liouville eigenvalue problems 1 p t p t u t g t f t u u 0 0 t 1 1 u 0 1 u 0 0 1 u 1 1 u 1 0 2 u 0 2 lim t 0 p t u t 0 2 u 1 2 lim t 1 p t u t 0 where 0 g p may be singular at t 0 and or 1 moreover f t x y may also have singularity at x 0 and or y 0 by using fixed point theory in cones an explicit interval for is derived such that for any in this interval the existence of at least one positive solution to the boundary value problem is guaranteed our results extend and improve many known results including singular and nonsingular cases

positive solutions and multiplicity of fourth order m point boundary value problems with two parameters abstract by means of calculation of the fixed point index in cone we study the existence of one or two positive solutions of the fourth order m point boundary value problems with two parameters

global structure of nodal solutions for a fourth order two point boundary value problem we consider the fourth order two point boundary value problem x kx lx a t f x 0 t 1 x 0 x 1 x 0 x 1 0 where a c 0 1 0 with a t 0 on any subinterval of 0 1 f c 1 r 0 r c r r satisfies f x x 0 for all x 0 we give conditions on the constants k l and the function f x that guarantee the existence and multiplicity results of nodal solutions the proofs of our main results are based upon disconjugate operator theory and the global bifurcation techniques

multiple solutions of some nonlinear fourth order beam equations abstract several new existence theorems on three solutions and infinitely many solutions for the following fourth order beam equation are obtained u 4 f t u t t 0 1 u 0 u 1 u 0 u 1 0 where f c 1 0 1 r 1 r 1 the morse theory is employed to discuss this problem

a sum operator equation and applications to nonlinear elastic beam equations and lane emden fowler equations article history this paper is concerned with an operator equation ax bx cx x on ordered banach spaces where a is an increasing concave operator b is an increasing sub homogeneous operator and c is a homogeneous operator the existence and uniqueness of its positive solutions is obtained by using the properties of cones and a fixed point theorem for increasing general concave operators as applications we utilize the fixed point theorems obtained in this paper to study the existence and uniqueness of positive solutions for two classes nonlinear problems which include fourth order two point boundary value problems for elastic beam equations and elliptic value problems for lane emden fowler equations

positive solution for m point boundary value problems of fourth order in this paper we consider the existence of positive solutions to the fourth order boundary value problem u u u f t u 0 t 1 u 0 i 1m 2aiu i u 1 i 1m 2biu i u 0 i 1m 2aiu i u 1 i 1m 2biu i where r i 0 1 ai bi 0 for i 1 2 m 2 are given constants satisfying some suitable conditions the proofs are based on the fixed point index theorem in cones

multiply sign changing solutions for fourth order nonlinear boundary value problems abstract this paper deals with the existence of sign changing solutions for the fourth order nonlinear boundary value problem u 4 f u u 0 t 1 u 0 u 1 u 0 u 1 0 where f r 2 r is a continuously odd function some conditions on f guaranteeing the existence and multiplicity of sign changing solutions are presented the existence and multiplicity conditions concern the eigenline of the associated two parameter linear eigenvalue problem the discussion is based on the fixed point index theory in cones and an anti symmetrical extension method of solution

constructive proof of existence for a class of fourth order nonlinear bvps a new existence proof of solutions for a class of fourth order nonlinear boundary value problems is proposed the proof of the main results is based on the reproducing kernel theorem it is worthwhile to point out that the method presented in this paper can be applied for the existence proof of diverse kinds of boundary conditions

measurements of the three dimensional shape of the rib cage a stereoradiographic method was developed to measure the three dimensional shape of the rib cage in vivo in order to provide descriptive data and to study symmetry in the normal population the method is also intended for use in description of rib asymmetry in scoliosis rib midlines were reconstructed from digitized points on lines drawn through the middle of each rib image in stereo radiographs of the rib cage the method relied on pairing points in one image with a corresponding point found in the second image the error term obtained from a direct linear transformation dlt reconstruction program was used for optimizing this correspondence the method was used on test objects of known shape where the standard deviation of measurement errors was found to be 0 72 mm studies in which different sets of points on the rib midlines were selected for digitizing showed that the precision of the method was 1 04 mm s d rib shape was described by intrinsic measurements arc and chord length maximum curvature and enclosed area and rib orientation by extrinsic measurements frontal and lateral angulations and posterior rib cage rotation no statistically significant rib shape asymmetry was found among ten subjects without spinal or thoracic abnormalities although a trend of inequality of rib angulation at all anatomical levels was observed

existence and uniqueness results for the bending of an elastic beam equation at resonance etude d un probleme non lineaire aux valeurs limites pour la flexion d une poutre elastique en appui simple aux deux extremites dans le cas de resonance theoremes d existence et d unicite

positive solutions of m point boundary value problems the second order m point boundary value problem x h x f x 0 0 x 1 0 0 1 i 1m 2ai i is considered under some conditions concerning the first eigenvalue of the relevant linear operator where i 0 1 with 0 1 2 m 2 1 ai 0 with i 1m 2ai 1 h x is allowed to be singular at x 0 and x 1 the existence of positive solutions and multiple positive solutions is obtained by means of fixed point index theory similarly conclusions hold for some other m point boundary value conditions

positive solutions of fourth order nonlinear singular boundary value problems abstract we consider the existence of positive solutions for the following fourth order singular sturm liouville boundary value problem 1 p t p t u t g t f t u 0 0 t 1 1 u 0 1 u 0 0 1 u 1 1 u 1 0 2 u 0 2 lim t 0 p t u t 0 2 u 1 2 lim t 1 p t u t 0 where g p may be singular at t 0 and or 1 moreover f t x may also have singularity at x 0 the existence and multiplicity theorems of positive solutions for the fourth order singular sturm liouville boundary value problem are obtained by using the first eigenvalue of the corresponding linear problems our results significantly extend and improve many known results including singular and nonsingular cases

multiple sign changing solutions for fourth order m point boundary value problems abstract in this paper we study the existence and multiplicity of nontrivial solutions for the fourth order m point boundary value problems making use of the theory of the fixed point index in a cone and the leray schauder degree under general conditions on nonlinearity we prove that there exist at least six different nontrivial solutions for the fourth order m point boundary value problems furthermore if the nonlinearity is odd we obtain that there exist at least eight different nontrivial solutions

modeling female and male rib geometry with logarithmic spirals in this study we present a novel six parameter shape model of the human rib centroidal path using logarithmic spirals it provides a reduction in parameter space from previous models of overall rib shape while simultaneously reducing fitting error by 34 and increasing curvature continuity furthermore the model directly utilizes geometric properties such as rib end to end span aspect ratio rib skewness and inner angle with the spine in its parameterization making the effects of each parameter on overall shape intuitive and easy to visualize the model was tested against 2197 rib geometries extracted from ct scans from a population of 100 adult females and males of uniformly distributed ages between 20 and 70 significant size and shape differences between genders were identified and shape model utility is demonstrated by the production of statistically average male and female rib shapes for all rib levels simulated mechanical loading of the resulting model rib shapes showed that the stiffness of statistically average male and female ribs matched well with the average rib stiffness from each separate population this in plane rib shape model can be used to characterize variation in human rib geometry seen throughout the population including investigation of the overall changes in shape and resultant mechanical properties that ribs undergo during aging or disease progression

existence of n solutions and or positive solutions to a semipositone elastic beam equation abstract the existence of n solutions and or positive solutions is established for a nonlinear fourth order two point boundary value problem where n is an arbitrary natural number and the nonlinear term has a nonpositive lower bound in mechanics the problem describes deformation of the elastic beam whose two ends are simply supported the main results show that the problem has at least n solutions and or positive solutions provided that the heights of the nonlinear term are appropriate on some bounded sets

multiple solutions of some fourth order boundary value problems abstract for some fourth order boundary value problems several new existence theorems on multiple positive negative and sign changing solutions are obtained the critical point theory and the supersolution and subsolution method are employed to discuss this problem

positive solutions of fourth order two point boundary value problems in this paper by using the krasnoselskii fixed point theorem we study the existence of one or multiple positive solution of the fourth order two point boundary value problem y 4 t f t y t y t y 0 y 1 y 0 y 1 0 we also give some examples to illustrate our results

triple positive solutions of three point boundary value problems for fourth order differential equations using the avery and peterson fixed point theorem we investigate the existence of three positive solutions for the fourth order three point boundary value problem u 4 t h t f t u t u t 00 0 x 1 and h t is sign changing on 0 1 the interesting point is that the nonlinear term is allowed to depend on u