Discontinuous semilinear differential equations and multiple valued maps

On Discontinuous Differential Equations

Theorem A. Let g : [0, T ]× IR 7→ IR be a bounded function. (i) If the map t 7→ g(t, x) is measurable for each x and the map x 7→ g(t, x) is continuous for each t, then the Cauchy problem (1.1) has at least one solution. (ii) If the map t 7→ g(t, x) is measurable for each x and the map x 7→ g(t, x) is Lipschitz continuous for each t, with a uniform Lipschitz constant, then the Cauchy problem (1...

Multivalued Semilinear Neutral Functional Differential Equations with Nonconvex-valued Right-hand Side

Semilinear Nonlocal Differential Equations with Delay Terms

The goal of this paper is to obtain the regularity and the existence of solutions of a retarded semilinear differential equation with nonlocal condition by applying Schauder’s fixed point theorem. We construct the fundamental solution, establish the Hölder continuity results concerning the fundamental solution of its corresponding retarded linear equation, and prove the uniqueness of solutions ...

Symmetry Coefficients of Semilinear Partial Differential Equations

We show that for any semilinear partial differential equation of order m, the infinitesimals of the independent variables depend only on the independent variables and, if m > 1 and the equation is also linear in its derivatives of order m− 1 of the dependent variable, then the infinitesimal of the dependent variable is at most linear on the dependent variable. Many examples of important partial...

First-Order Singular and Discontinuous Differential Equations