A semi-analytical approach to the elastic nonlinear stability analysis of rectangular plates is developed. Arbitrary boundary conditions and general out-of-plane and in-plane loads are considered. The geometrically nonlinear formulation for the elastic rectangular plate is derived using the thin plate theory with the nonlinear von Kármán strains and the variational multi-term extended Kantorovi...

We consider the nonlocal Hénon-Gelfand–Liouville problem $$\begin{aligned} (-\Delta )^s u = |x|^a e^u\quad \mathrm {in}\quad \mathbb {R}^n, \end{aligned}$$ for every $$s\in (0,1)$$ , $$a>0$$ and $$n>2s$$ . prove a monotonicity formula solutions of above equation using rescaling arguments. apply this together with blow-down analysis arguments technical integral estimates to establish non-existen...

Three different spline-based approaches for solving Bratu and Bratu-type equations are presented. The classical cubic spline collocation method, an adaptive spline collocation on nonuniform partitions, and an optimal collocation method are derived for solving Bratu-type equations. Numerical examples are presented to verify the efficiency and accuracy of these methods when compared to other nume...

In this paper, we consider applications of the connection between soliton theory and commuting nonselfadjoint operator theory, established by Livšic Avishai. An approach to inverse scattering problem wave equations is presented, based on colligation (or vessel theory) in case bounded operators a Hilbert space, when one belongs larger class nondissipative with asymptotics corresponding curves. T...

a class of new methods based on a septic non-polynomial spline function for the numerical solution one-dimensional bratu's problem are presented. the local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. the inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. associated bound...

We give an interpretation of the hemisphere rigidity theorem Hang-Wang in framework Gelfand problem. More precisely, showed that for a metric $ g conformal to standard g_0 on S^{n}_{+} with R\geq n(n-1) and whose boundary coincides g_0|_{\partial S^{n}_{+}} $, then = $. This is related classical problem, which investigates -\Delta u \lambda g(u) certain nonlinearity bounded region \Omega \subse...

This paper explores the reconstruction of drift or diffusion coefficients of a scalar stochastic diffusion processes as it starts from an initial value and reaches, for the first time, a threshold value. We show that the distribution function derived from repeated measurements of the first-exit times can be used to formally partially reconstruct the dynamics of the process. Upon mapping the rel...