Let Ω ⊂ R be a bounded domain with smooth boundary, and let K : [0,+∞[→ R be a given continuous function. If n ≥ 2, we denote by A the class of all Carathéodory functions φ : Ω×R → R such that sup (x,t)∈Ω×R |φ(x, t)| 1 + |t|q < +∞ , where 0 < q < n+2 n−2 if n > 2 and 0 < q < +∞ if n = 2. While, when n = 1, we denote by A the class of all Carathéodory functions φ : Ω ×R → R such that, for each r...

In recent years, various Kirchhoff type problems have been extensively investigated by many authors due to their theoretical and practical importance, such problems are often referred to as being nonlocal because of the presence of the integral over the entire domain Ω. It is well known that this problem is analogous to the stationary problem of a model introduced by Kirchhoff [1]. More precise...

In this article, we obtain the existence and infinitely many nontrivial solutions for a class of nonlinear critical anisotropic elliptic equations involving variable exponents two real parameters, via combining variational method, concentration-compactness principle exponent under suitable assumptions on nonlinearities.

In recent years it has been trying that with regard to the question of computational complexity of discrete logarithm more strength and less in the elliptic curve than other hard issues, applications such as elliptic curve cryptography, a blind  digital signature method, other methods such as encryption replacement DLP. In this paper, a new blind digital signature scheme based on elliptic curve...

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...

We carry out an investigation of the existence infinitely many solutions to a fractional p-Kirchhoff-type problem with singularity and superlinear nonlinearity homogeneous Dirichlet boundary condition. Further, solution(s) will be proved bounded weak comparison principle has also been proved. A ‘\(C^1\) versus \(W_0^{s,p}\)’ analysis discussed.

In this article, we study a system of viscoelastic parabolic type Kirchhoff equation with multiple nonlinearities. We obtain finite time blow up solutions and exponential growth solution negative initial energy.