dynamic stability of stiffened laminated composite plates and shells subjected to in plane pulsating forces abstract the dynamic stability of laminated composite stiffened or non stiffened plates and shells due to periodic in plane forces at boundaries is investigated in this paper the 3 d degenerated shell element and 3 d degenerated curved beam element are used to model plates shells and stiffeners respectively the characteristic equations for the natural frequencies buckling loads and their corresponding mode shapes are obtained from the finite element equations of motion then the method of hill s infinite determinants or the method of multiple scales is applied to analyze the dynamic instability regions numerical results are presented to demonstrate the effects of various parameters such as skew angle lamination scheme stiffening scheme in plane force type and the curvature of the cylindrical shells on the dynamic stability of stiffened and non stiffened plates and shells subjected to in plane pulsating forces at boundaries

asymptotic behavior of large solutions to p laplacian of bieberbach rademacher type abstract by the karamata regular variation theory and the method of lower and upper solutions we establish the asymptotic behavior of boundary blow up solutions of the quasilinear elliptic equation div u p 2 u b x f u in a bounded r n subject to the singular boundary condition u x where the weight b x is non negative and non trivial in which may be vanishing on the boundary or go to unbounded the nonlinear term f is a varying function at infinity whose variation at infinity is not regular

lifespan of solutions to semilinear damping wave equations in de sitter spacetime abstract this paper studies blowup phenomena for two kind of initial value problem of semilinear damping wave equations in de sitter spacetime the first problem comes from the latter problem of conjecture of strauss in de sitter spacetime and the second problem arises from the latter problem of conjecture of glassey in de sitter spacetime we give blowup and lifespan of solutions on those two problems comparing with non damping case established in yan 2018 one can see that the damping term with a positive bounded time dependent coefficient does not effect blowup of solutions meanwhile we establish a new ode blowup result concerning damping term

asymptotic behavior of large solution to elliptic equation of bieberbach rademacher type with convection terms we analyze the asymptotic behavior of solutions to nonlinear elliptic equation du u q b x f u in w subject to the singular boundary condition u x as dist x email protected 0 where w is a smooth bounded domain in r n email protected email protected rv r r 0 for some email protected c 2 a lim u l u and l nrv 1 our approach employs karamata regular variation theory combined with the method of lower and supper solution

asymptotic behavior of entire large solutions to semilinear elliptic equations abstract in this paper by using karamata regular variation theory we study the exact asymptotic behavior of entire large solutions to u b x f u x r n n 3 where b c r n is nonnegative and nontrivial in r n f c 0 is positive and non decreasing on 0 which satisfies keller osserman condition and is rapidly varying or regularly varying at infinity with index 1

dynamic stability of stiffened laminated composite plates and shells subjected to in plane pulsating forces the dynamic stability of laminated composite stiffened or non stiffened plates and shells due to periodic in plane forces at boundaries is investigated in this paper a three dimensional 3 d degenerated shell element and a 3 d degenerated curved beam element are used to model plates shells and stiffeners respectively the characteristic equations to find the natural frequencies buckling loads and their corresponding mode shapes are obtained from the finite element equation of motion then the method of hill s infinite determinants or the method of multiple scales is applied to analyse the dynamic instability regions numerical results are presented to demonstrate the effects of various parameters such as skew angle lamination scheme stiffened scheme in plane force type and curvature of cylindrical shell on the dynamic stability of stiffened and non stiffened plates and shells subjected to in plane pulsating forces at boundaries

boundary blow up in nonlinear elliptic equations of bieberbach rademacher type the research of the first author was carried out at victoria university melbourne with the support of the australian government through detya the second author has been supported by grant 2 cex06 11 18 2006

pointwise growth and uniqueness of positive solutions for a class of sublinear elliptic problems where bifurcation from infinity occurs in this paper we analyze the uniqueness and the pointwise growth of the positive solutions of a nonlinear elliptic boundary value problem of general sublinear type with a weight function multiplying the nonlinearity when this function vanishes on some subdomain the problem exhibits a bifurcation from infinity in this case almost nothing is known about the pointwise growth of the positive solutions as the parameter approaches the critical value where the bifurcation from infinity occurs in this work we show that the positive solutions grow to infinity in the region where the weight function vanishes and that on its support they stabilize to the minimal positive solution of the original equation subject to infinite dirichlet boundary conditions this behavior provides us with the uniqueness of the positive solution near the value of the parameter where the bifurcation from infinity occurs also we solve the problem using spectral collocation methods coupled with path following techniques to show how the main uniqueness result is optimal throughout the paper the mathematical analysis aids the numerical study and the numerical study confirms and illuminates the analysis

large solution to nonlinear elliptic equation with nonlinear gradient terms abstract the aim of this paper is to study the qualitative behavior of large solutions to the following problem u a x u q b x f u x u x x here a x c is a positive function with 0 1 b x c is a non negative function and may be singular near the boundary or vanish on the boundary and the nonlinear term f is a varying function whose variation at infinity is not regular we focus our investigation on the existence and asymptotic behavior close to the boundary of large solutions by karamata regular variation theory and the method of upper and lower solution the main results of this paper emphasize the central role played by the gradient term u q and the weight functions a x and b x

boundary asymptotic and uniqueness of solutions to the p laplacian with infinite boundary values we prove boundary asymptotics to solutions of weighted p laplacian equations that take infinite value on the boundary of a bounded domain uniqueness of such solutions would then follow as a consequence our results extend previously known results by allowing weights that are unbounded in the domain

boundary blow up solutions to degenerate elliptic equations with non monotone inhomogeneous terms abstract given a non negative and non trivial continuous real valued function h on 0 such that h x 0 0 for all x we study the boundary value problem bvp u h x u in u on where r n n 2 is a bounded domain and is the laplacian a degenerate elliptic operator in this paper we investigate conditions on the inhomogeneous term h x t under which problem bvp admits a solution or fails to admit a solution in c some notable features of this work are that h x t is not required to have any special structure and no monotonicity condition is imposed on h x t furthermore h x t may be allowed to vanish in either of the variables

the second expansion of the unique vanishing at infinity solution to a singular elliptic equation abstract this paper is considered with the second expansion of the unique vanishing at infinity solution to u b x g u x r n n 3 where b c r n is nonnegative and may be supercritical attenuation or critical attenuation at infinity g c 1 0 0 is non increasing on 0 with lim s 0 g s and g is normalized regularly varying at zero with index 1

the second order expansion of boundary blow up solutions for infinity laplacian equations abstract in this paper by using karamata regular variation theory and a perturbed argument we study the second order expansion of viscosity solutions to boundary blow up elliptic problem u b x f u x u where is a bounded domain with c 2 boundary in r n b c is non negative and non trivial in f c 1 0 is a normalized regularly varying function at infinity with index 3

blow up rates of large solutions for infinity laplace equations in this paper by constructing suitable comparison functions we mainly give the boundary behavior of solutions to boundary blow up elliptic problems u b x f u x u where is a bounded domain with smooth boundary in r n the operator is the laplacian b c which is positive in and may be vanishing on the boundary and rapidly varying near the boundary and the nonlinear term f is a varying function at infinity whose variation at infinity is not regular

positive solutions of an elliptic partial differential equation on rn abstract in this paper we discuss the existence nonexistence and uniqueness of positive solutions of a one parameter family of elliptic partial differential equations on r n n 2 these equations are of interests in mathematical biology and riemannian geometry our approach are based on variational arguments and comparison principles

dynamic stability analysis of composite laminated cylindrical shells via the mesh free kp ritz method abstract in this paper a novel numerical technique is developed for the dynamic stability analysis of composite laminated cylindrical shells under static and periodic axial forces the mesh free kernel particle kp estimate is employed in hybridized form with harmonic functions to approximate the 2 d transverse displacement field a system of mathieu hill equations is obtained through the application of the ritz minimization procedure to the energy expressions the principal instability regions are then analyzed via bolotin s first approximation the mesh free kp ritz method is validated through comparison with existing available numerical data taken from open literature effects of boundary conditions and lamination schemes on the instability regions are also examined in detail

indirect inference in structural econometric models this paper considers parametric inference in a wide range of structural econometric models it illustrates how the indirect inference principle can be used in the inference of these models specifically we show that an ordinary least squares ols estimation can be used as an auxiliary model which leads to a method that is similar in spirit to a two stage least squares 2sls estimator monte carlo studies and an empirical analysis of timber sale auctions held in oregon illustrate the usefulness and feasibility of our approach

dynamic instability of stiffened plates subjected to non uniform harmonic in plane edge loading the dynamic instability characteristics of stiffened plates subjected to in plane partial and concentrated edge loadings are studied using finite element analysis in the structural modelling the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained the method of hill s infinite determinants is applied to determine the dynamic instability regions numerical results are presented to study the effects of various parameters such as static load factor aspect ratio boundary conditions stiffening scheme and load parameters on the principal instability regions of stiffened plates using bolotin s method the results show that location size and number of stiffeners have a significant effect on the location of the boundaries of the principal instability region

the exact blow up rates of large solutions for semilinear elliptic equations abstract in this paper combining the method of lower and upper solutions with the localization method we establish the boundary blow up rate of the large positive solutions to the singular boundary value problem u b x f u x u x x where is a smooth bounded domain in r n the weight function b x is a non negative continuous function in the domain which vanishes on the boundary of the underlying domain at different rates according to the point of the boundary f u is locally lipschitz continuous satisfying the keller osserman condition and f u u is increasing on 0 it is worth emphasizing that we obtain the main results for a large class of nonlinear terms f which is regularly varying at infinity with index p r that is for all 0 lim u f u f u p instead of the restriction f u h u p for sufficiently large u and some positive constants h 0 p 1 as in the series of papers of j l gomez

transient analysis of ring stiffened composite cylindrical shells with both edges clamped abstract a theoretical method is developed to investigate the effects of ring stiffeners on vibration characteristics and transient responses for the ring stiffened composite cylindrical shells subjected to the step pulse loading love s thin shell theory combined with the discrete stiffener theory to consider the ring stiffening effect is adopted to formulate the theoretical model the ring stiffeners are laminated with a composite material and have a uniform rectangular cross section the rayleigh ritz procedure is applied to obtain the frequency equation the modal analysis technique is used to develop the analytical solutions of the transient response the analysis is based on an expansion of the loads displacements in the double fourier series that satisfy the boundary conditions the effect of stiffener s eccentricity number size and position on transient response of the shells is examined the theoretical results are verified by comparison with fem results

the second expansion of large solutions for semilinear elliptic equations abstract in this paper we analyze the influence of the domain geometry in the second expansion of solutions to the boundary blow up elliptic problem u b x f u u 0 x u where is a bounded domain with c 4 smooth boundary in r n b c which is positive in and may be vanishing on the boundary and f is normalized regularly varying at infinity with index p p 1

dynamic stability of rectangular plates subjected to pulsating follower forces the dynamic stability of isotropic and nonsymmetric laminated plates with four free edges subjected to pulsating follower forces is discussed the results are obtained using the first order shear deformation theory the discretized equation of motion is obtained by the finite element method and then the method of multiple scales is adopted to investigate the dynamic instability regions the effects of poisson ratio as well as aspect and thickness ratios on the dynamic instability region for isotropic plates are investigated the influences of aspect ratio lamination angle and the number of layers for nonsymmetric cross ply and angle ply laminated plates are also studied

boundary asymptotic behavior and uniqueness of large solutions to quasilinear elliptic equations we study the existence uniqueness and exact asymptotic behavior of solutions near the boundary to a class of quasilinear elliptic equations div u p email protected u email protected u b x f u email protected where l is a real number and b x 0 in w and vanishes on email protected the uniqueness of such a solution follows as a consequence of the exact blow up rate

a probabilistic approach to one class of nonlinear differential equations we establish connections between positive solutions of one class of nonlinear partial differential equations and hitting probabilities and additive functionals of superdiffusion processes as an application we improve results on superprocesses by using the recent progress in the theory of removable singularities for differential equations

on boundary blow up solutions to equations involving the laplacian abstract given a non negative continuous function h on r such that h x 0 0 for all x h x t 0 in 0 and h x t non decreasing in t for each x we study the boundary value problem u h x u in u on where r n n 2 is a bounded domain and is the laplacian a degenerate elliptic operator we provide sufficient conditions on h under which the above problem admits a solution or fails to admit a solution a necessary and sufficient condition on f is given for a solution to exist in the special case when h x t b x f t in the latter case an asymptotic boundary behavior of solutions will be studied as an application a sufficient condition on f will be given to ensure the uniqueness of solutions in case b is a constant

boundary behavior of solutions for the degenerate logistic type elliptic problem with boundary blow up abstract by the karamata regular variation theory and constructing comparison function we show the exact asymptotic behavior of solutions for the degenerate logistic type elliptic problem with boundary blow up

uniqueness of boundary blow up solutions on unbounded domain of rn abstract in this paper we consider the existence of positive solutions of the degenerate logistic type elliptic equation u a x u b x f u x r n d u d where n 2 d r n is a bounded smooth domain and a x b x are continuous functions on r n with b x 0 b x 0 especially b x 0 on d and f u c 0 we show that under rather general conditions on a x and b x for large x and f u behaves like u q where q 1 without the behavior of b x near the boundary d it will be shown that there exists a unique positive solution our results improve the corresponding ones in w dong pang uniqueness of boundary blow up solutions on exterior domain of r n j math anal appl 330 2007 654 664 and y du l ma logistic type equations on r n by a squeezing method involving boundary blow up solutions j london math soc 2 64 2001 107 124

boundary blow up elliptic problems of bieberbach and rademacher type with nonlinear gradient terms abstract by a perturbation method and constructing comparison functions we show the exact asymptotic behaviour of solutions near the boundary to nonlinear elliptic problems u u q b x e u x u where is a bounded domain with smooth boundary in r n q 0 b is non negative and non trivial in which may be vanishing on the boundary

boundary blow up quasilinear elliptic problems of the bieberbach type with nonlinear gradient terms abstract by a perturbation method and by constructing comparison functions we show the exact asymptotic behaviour of solutions near the boundary of the quasilinear elliptic problem div u m 2 u u x q m 1 b x e u x x u where is a c 2 bounded domain with a smooth boundary in r n n 2 m 1 q 0 b is nonnegative and nontrivial in which may vanish on the boundary

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

asymptotic behavior of large solution for boundary blowup problems with non linear gradient terms let email protected r n n 3 be a bounded domain with smooth boundary we show the asymptotic behavior of boundary blowup solutions to non linear elliptic equation du u q b x f u in w subject to the singular boundary condition u x as dist x email protected 0 f is c varying at our analysis is based on the karamata regular variation theory combined with the method of lower and supper solution

boundary blow up rates of large solutions for elliptic equations with convection terms abstract by karamata regular variation theory a perturbation method and constructing comparison functions we show the exact asymptotic behavior of large solutions to the semilinear elliptic equations with convection terms u u q b x f u x u x x where is a smooth bounded domain in r n the weight function b x is a non negative continuous function in the domain which may be vanishing on the boundary or be singular on the boundary f u c 2 0 is increasing on 0 satisfying the keller osserman condition and regularly varying at infinity with index 1