The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form Ku'' + M(|A (1/2) u|(2))Au + g(u') = 0 under suitable assumptions on K, A, M(·), and g(·). Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipation g. Lastly, numerical simulations ...

Let G be a simple connected graph with n ≤ 2 vertices and m edges, and let μ1 ≥ μ2 ≥...≥μn-1 >μn=0 be its Laplacian eigenvalues. The Kirchhoff index and Laplacian-energy-like invariant (LEL) of graph G are defined as Kf(G)=nΣi=1n-1<...

We continue our investigation of E-operators, in particular their connection with G-operators; these differential operators are fundamental in understanding the diophantine properties of Siegel’s E and G-functions. We study in detail microsolutions (in Kashiwara’s sense) of Fuchsian differential operators, and apply this to the construction of basis of solutions at 0 and∞ of any E-operator from...

Biogeography Based Optimization (BBO) is a recently introduced optimization technique based on science of biogeography, i. e. , study of distribution of biological species over space and time. In BBO, potential solutions of a problem are grouped in integer vectors known as habitats. Feature, i. e. , Suitability Index Variable (SIV), sharing among various habitats is made to occur with migration...

In this paper, we study two classes of Kirchhoff-type problems set on a double-phase framework. That is, the functional space where finding solutions coincides with Musielak–Orlicz–Sobolev $$W^{1,{\mathcal {H}}}_0(\Omega )$$ , modular function $${\mathcal {H}}$$ related to so-called operator. Via variational approach, provide existence and multiplicity results.