In this work we obtain some continuity properties on the parameter p at p = 2 for the Takeuchi-Yamada problem which is a degenerate p-Laplacian version of the Chafee-Infante problem. We prove the continuity of the flows ...

In this paper, we study the behavior as p→ ∞ of eigenvalues and eigenfunctions of a system of p-Laplacians, that is (Formula presented.) in a bounded smooth domain Ω. Here α+ β= p. We assume that α/p→Γ and β/p→1-Γ as p→ ∞ ...

We prove the existence of an unbounded branch of solutions to the nonlinear non-local equation (Equation presented) bifurcating from the first eigenvalue. Here (-Δ)s p denotes the fractional p-Laplacian and Ω ⊂ ℝ1 is a ...

In this note we study the limit as p(x) → ∞ of solutions to −∆p(x)u = 0 in a domain Ω, with Dirichlet boundary conditions. Our approach consists in considering sequences of variable exponents converging uniformly to +∞ and ...

We deal with the clustering problem in a metric graph. We look for two clusters, and to this end, we study the first nonzero eigenvalue of the p Laplacian on a quantum graph with Newmann or Kirchoff boundary conditions on ...

Our propose here is to provide a Hopf lemma and a strong minimum principle for weak supersolutions of (−Δp)su=c(x)|u|p−2u in Ω where Ω is an open set of RN, s∈(0,1), p∈(1,+∞), c∈C(Ω‾) and (−Δp)s is the fractional p-Laplacian.

In this article we extend the Sobolev spaces with variable exponents to include the fractional case, and we prove a compact embedding theorem of these spaces into variable exponent Lebesgue spaces. As an application we ...

This paper is concerned with the energy decay for a class of plate equations with memory and lower order perturbation of p-Laplacian type, utt+?2u-?pu+?0tg(t-s)?u(s)ds-?ut+f(u)=0inOXR+, with simply supported boundary ...

In this paper we extend two nowadays classical results to a nonlinear Dirichlet problem to equations involving the fractional p-Laplacian. The first result is an existence in a non-resonant range more specific between the ...