Translating solutions for a class of quasilinear parabolic initial boundary value problems in Lorentz–Minkowski plane R12

On the existence of nonnegative solutions for a class of fractional boundary value problems

‎In this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎By applying Kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary BVP formulated by truncating the response function‎. ‎Then the Arzela--Ascoli theorem is used to take $C^1$ ...

Initial - Boundary Value Problems for Parabolic Equations

Degenerate Parabolic Initial-Boundary Value Problems*

in Hilbert space and their realizations in function spaces as initial-boundary value problems for partial differential equations which may contain degenerate or singular coefficients. The Cauchy problem consists of solving (1.1) subject to the initial condition Jdu(0) = h. We are concerned with the case where the solution is given by an analytic semigroup; it is this sense in which the Canchy p...

Multiplicity of solutions for quasilinear elliptic boundary-value problems

This paper is concerned with the existence of multiple solutions to the boundary-value problem −(φp(u )) = λφq(u) + f(u) in (0, 1) , u(0) = u(1) = 0 , where p, q > 1, φx(y) = |y| y, λ is a real parameter, and f is a function which may be sublinear, superlinear, or asymmetric. We use the time map method for showing the existence of solutions.

Maximal regularity and quasilinear parabolic boundary value problems

∂tw +A(v)w = f(v) in J̊ , w(0) = 0 has a unique solution w = w(v) ∈W(J). Clearly, a fixed point of the map v 7→ w(v) is a solution of (1). Fixed point arguments of this type are, of course, omnipresent in the study of evolution equations of type (1). The new feature of our work, which distinguishes it from all previous investigations, is that we assume that W(J) is a maximal regularity space and...