We deal with Dirichlet's problem for second order quasilinear non-divergence form elliptic equations with discontinuous coefficients. First we state suitable structure, growth, and regularity conditions ensuring solvability ...

We prove existence, local uniqueness and asymptotic estimates for boundary layer solutions to singularly perturbed problems of the type $\varepsilon^2 u''=f(x,u,\varepsilon u',\varepsilon), 0< x

We consider boundary value problems for 1D autonomous damped and delayed semilinear wave equations of the type ∂2tu(t,x)−a(x,λ)2∂2xu(t,x)=b(x,λ,u(t,x),u(t−τ,x),∂tu(t,x),∂xu(t,x)),x∈(0,1) with smooth coefficient functions ...

The Neumann boundary value problem for a class of singularly perturbed integro-parabolic equations is considered. An asymptotic expansion of a new class of solutions of moving front type is constructed, and a theorem of ...