We consider the homogeneous Dirichlet problem for the anisotropic parabolic equation ut−∑i=1NDx(|Dxu|pDxu)=f(x,t) in the cylinder Ω×(0,T), where Ω⊂RN, N≥2, is a parallelepiped. The exponents of nonlinearity pi are given ...

Arora, Rakesh; Shmarev, Sergey(Springer-Verlag Italia s.r.l., 2022-11-30)

We study the homogeneous Dirichlet problem for the equation ut-div(F(z,∇u)∇u)=f,z=(x,t)∈QT=Ω×(0,T),where Ω ⊂ RN, is a bounded domain with ∂Ω ∈ C2, and F(z, ξ) = a(z) | ξ| p(z)-2+ b(z) | ξ| q(z)-2. The variable exponents ...

In this paper we study quasilinear elliptic equations driven by the double phase operator involving a Choquard term of the form [Formula presented] where Lp,qa is the double phase operator given by Lp,qa(u)≔div(|∇u|p−2∇u ...

In this paper, we study multiplicity results for double phase problems of Kirchhoff type with right-hand sides that include a parametric singular term and a nonlinear term of subcritical growth. Under very general assumptions ...