Abstract A nonlinear viscoelastic Kirchhoff-type equation with Balakrishnan–Taylor damping and distributed delay is studied. By the energy method we establish general decay rate under suitable hypothesis.

In this article, we study the nonlocal p(x)-Laplacian problem

Copyright q 2010 Bitao Cheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. By using variational methods, we study the multiplicity of solutions for Kirchhoff type problems −a b Ω |∇u| 2 Δu f x, u, in Ω; u 0, on ∂Ω. Existe...

Jemal Peradze Faculty of Exact and Natural Sciences, I. Javakhishvili Tbilisi State University, 2 University St., 0143 Tbilisi, Georgia Correspondence should be addressed to Jemal Peradze, j [email protected] Received 5 March 2009; Accepted 22 June 2009 Recommended by James Buchanan A boundary value problem is posed for an integro-differential beam equation. An approximate solution is found usi...

A m,n -bipartite graph is a bipartite graph such that one bipartition has m vertices and the other bipartition has n vertices. The tree dumbbell D n, a, b consists of the path Pn−a−b together with a independent vertices adjacent to one pendent vertex of Pn−a−b and b independent vertices adjacent to the other pendent vertex of Pn−a−b. In this paper, firstly, we show that, among m,n bipartite gra...

Using the mountain pass theorem combined with the Ekeland variational principle, we obtain at least two distinct, non-trivial weak solutions for a class of p(x)-Kirchhoff type equations with combined nonlinearities. We also show that the similar results can be obtained in the case when the domain has cylindrical symmetry.

In this paper, we study uniform exponential stabilization of the vibrations of the Kirchhoff type wave equation with acoustic boundary in a bounded domain in Rn. To stabilize the system, we incorporate separately, the passive viscous damping in the model as like Gannesh C. Gorain [1]. Energy decay rate is obtained by the exponential stability of solutions by using multiplier technique.

In this work, we consider the blow up of solutions for viscoelastic wave equation Kirchhoff type with variable exponents. The present result in work improve previous literature.

We study the existence of ground states to a nonlinear fractional Kirchhoff equation with an external potential V . Under suitable assumptions on V , using the monotonicity trick and the profile decomposition, we prove the existence of ground states. In particular, the nonlinearity does not satisfy the Ambrosetti-Rabinowitz type condition or monotonicity assumptions.

In this article, we consider the multiplicity of positive solutions for a class of Kirchhoff type problems with concave and convex nonlinearities. Under appropriate assumptions, we prove that the problem has at least two positive solutions, moreover, one of which is a positive ground state solution. Our approach is mainly based on the Nehari manifold, Ekeland variational principle and the theor...