This paper is concerned with the existence and multiplicity of weak solutions for a p(x)-Kirchhoff problem by using variational method genus theory. We prove simplicity boundedness principal eigenvalue.

Abstract In this article, we study discrete Kirchhoff-type problems when the nonlinearity is resonant at both zero and infinity. We establish a series of results on existence nontrivial solutions by combining variational method with Morse theory. Several examples are provided to illustrate applications our results.

The first and second Rayleigh-Sommerfeld diffraction theories, together with the Kirchhoff diffraction theory, are widely used in the formulation of optical diffraction problems [ 1 ]. They arise in the context of the half-space boundary-value problem of scalar wave theory; all sources of the optical field are assumed to be located in the Z~< 0 half-space, and the Z > 0 half-space is taken to b...

We consider a two phase elastic thin film with soft inclusions subject to bending dominated deformations. The (void) may comprise asymptotically small droplets within the matrix. perform dimension reduction analysis and obtain novel ‘Blake-Zisserman-Kirchhoff’ functional on natural space of ‘flat fractured’ two-dimensional isometric immersions that combines Kirchhoff's classical plate theory Bl...

This paper deals with the isogeometric analysis using B-splines of space rods subject to Kirchhoff-Love hypotheses. A multi-patch isogeometric approach for the numerical analysis of the three-dimensional Kirchhoff-Love rod theory is developed. We use Bezier and B-splines interpolations and we show that they are able to attain very good accuracy for rod structures, particularly for developing a ...

The hyper-Kirchhoff index is introduced when the hyper-Wiener operator is applied to the resistance-distance matrix of a connected graph. We give lower and upper bounds for the hyper-Kirchhoff index, and determine the n-vertex unicyclic graphs with the smallest, the second and the third smallest as well as the largest, the second and the third largest hyper-Kirchhoff indices for n ≥ 5. We also ...

Abstract: We compare two mathematical theories that address duality between cycles and vertex-cuts of graphs in geometric settings. First, we propose a rigorous definition of a new type of graph, vector graphs. The special case of R2-vector graphs matches the intuitive notion of drawing graphs with edges taken as vectors. This leads to a discussion of Kirchhoff graphs, as originally presented b...

In this sequel to a rather recent paper on the classical problem of Helmholtz–Kirchhoff flows by Vic. V. Sychev, TsAGI Science Journal 41(5), 531–533 (2010), the representation of the flow far from the body and its specific implications discussed in that study are revisited. Here the concise derivation of these findings resorts to well-known Levi-Cività’s method and, alternatively, only fundame...

We consider the interaction of two vortex patches (elliptic Kirchhoff vortices) which move in an unbounded volume of an ideal incompressible fluid. A moment second-order model is used to describe the interaction. The case of integrability of a Kirchhoff vortex and a point vortex by the variable separation method is qualitatively analyzed. A new case of integrability of two Kirchhoff vortices is...