Proceedings of the Fifth International Colloquium on Differential Equations

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This work explores various advanced topics in mathematical analysis and differential equations. It addresses the inverse scattering problem for the wave equation with discontinuous wave speeds and presents difference methods for impulsive partial differential equations. The text examines radially symmetric solutions of semilinear elliptic equations and introduces weighted Poincaré-type inequalities in multiple dimensions. It discusses matrix nonstationary semigroups and critical points theory, applying these concepts to nonlinear wave equations. The existence of decreasing positive solutions for linear differential equations with delays is investigated, alongside equations in nonlinear membrane theory. Additional topics include the dynamics of clustering neural networks, elliptic equations with measure data, and a novel b-spline finite element method for the advection-diffusion equation. The work delves into coupled elliptic systems relevant to fuel cell modeling and compares deficiency indices of differential expressions. It covers reproducing kernels, inverse formulas for Laplace transforms, and Hankel transforms related to dust diffusion. Asymptotic volume nullification of singular diffusions is analyzed, as well as conditions for the absence of positive solutions in differential inequalities with distributed delays. The stability of large-scale impulsive systems and heat conduction in mediums with thin shells are also dis