Dirichlet problem with Φ-Laplacian and mixed singularities

Abstract

Assume that A1, A2 ⊂ ℝ are closed intervals containing 0, ϕ is an increasing odd homeomorphism with ϕ (ℝ) = ℝ, and T ∈ (0, ∞). We study a singular Dirichlet problem of the form {fx080-01} and prove the existence of its smooth solution satisfying the conditions {fx080-02}, where ƒ satisfies the Carathéodory conditions on the set (0, T) × D and can have time singularities at t = 0 and t = T and space singularities at x = 0, y = 0.