On Discontinuous First Order Implicit Boundary Value Problems

Existence of the Solution of an Implicit Integro-Differential Equation of Order One

“…This work is motivated by an increasing interest in implicit di¤erential equations under various initial and boundary conditions. A good amount of nice works can be found in the literature concerning the existence and uniqueness results for implicit di¤erential equations, see [2,5,6,7,10] and the references cited in the papers. H. Ishii [8] concerned with the existence of solutions of nonlinear first order scalar partial di¤erential equations (Hamilton-Jacobi equations) F ðx; u; DuÞ ¼ 0; in W; ð1:3Þ where W is an open subset of R N , F A CðW Â R Â R N ; RÞ, u : W !…”

Peano's Theorem for Implicit Differential Equations

“…denoted by CP , consisting of the implicit ordinary differential equation where m g N. This consideration is motivated by an increasing interest in implicit differential equations under various initial and boundary condi-Ž w x . tions cf., e.g., 3,6,7,11,14,15, 17᎐20, 26᎐28, 32᎐36 .…”