this paper studies a fractional boundary value problem of nonlineardifferential equations of arbitrary orders. new existence and uniquenessresults are established using banach contraction principle. other existenceresults are obtained using schaefer and krasnoselskii fixed point theorems.in order to clarify our results, some illustrative examples are alsopresented.

Singular boundary conditions are formulated for non-selfadjoint Sturm-Liouville operators with singularities and turning points. For boundary value problems with singular boundary conditions properties of the spectrum are studied and the completeness of the system of root functions is proved.

In this paper, the degenerate scale for plate problem is studied. For the continuous model, we use the null-field integral equation, Fourier series and the series expansion in terms of degenerate kernel for fundamental solutions to examine the solvability of BIEM for circular thin plates. Any two of the four boundary integral equations in the plate formulation may be chosen. For the discrete mo...

Twizell, E.H. and S.A. Matar, Numerical methods for computing the eigenvalues of linear fourth-order boundary-value problems, Journal of Computational and Applied Mathematics 40 (1992) 115-125. Novel finite-difference methods are developed for approximating the cigenvalues of three types of linear, fourth-order, two-point, boundary-value problems. The fourth-order differential equation is trans...

The classical theory of strictly hyperbolic boundary value problems has received several extensions since the 70’s. One of the most noticeable is the result of Metivier establishing that Majda’s "block structure condition" for constantly hyperbolic operators, which implies well-posedness for the initial boundary value problem (IBVP) with zero initial data. The well-posedness of IBVP with non ze...

Transformed normal random fields are convenient models, e.g., for random material property fields obtained from microstructure analysis. In the context of the stochastic finite-element (FE) method, discretization of non-normal random fields by polynomial chaos expansions has been frequently employed. This introduces a non-linear relationship between the system matrix and normal random variables...

We solve a class of initial boundary value problems posed in a time-dependent convex domain for the sine-Gordon equation and for its linearized version. We give an explicit integral representation of the solution by using the Fokas transform method; this representation, which has an explicit exponential x and t dependence, is obtained by solving a d-bar problem in the complex plane. This d-bar ...

Fast direct methods are presented for the solution of linear systems arising in highorder, tensor-product orthogonal spline collocation applied to separable, second order, linear, elliptic partial di erential equations on rectangles. The methods, which are based on a matrix decomposition approach, involve the solution of a generalized eigenvalue problem corresponding to the orthogonal spline co...

On the half line 0; 1) we study rst order diierential operators of the form B 1 i d dx + Q(x); where B := B 1 0 0 ?B 2 ; B 1 ; B 2 2 M(n; C) are self{adjoint positive deenite matrices and Q : R + ! M(2n; C); R + := 0; 1); is a continuous self{adjoint oo{diagonal matrix function. We determine the self{adjoint boundary conditions for these operators. We prove that for each such boundary value pro...