Two solutions to Kirchhoff-type fourth-order implusive elastic beam equations

Positive Solutions for a Nonlocal Fourth Order Equation of Kirchhoff Type

Existence and multiplicity of positive solutions for the fourth order equation u′′′′ − M( ∫ 1 0 |u ′|2 dx)u′′ = q(x)f(x, u, u′), which models simply supported extensible beams, are considered using fixed point theorems in cones of ordered Banach spaces.

Multiplicity Results for Perturbed Fourth-order Kirchhoff-type Problems

Compactness of solutions to some geometric fourth-order equations

We prove compactness of solutions to some fourth order equations with exponential nonlinearities on four manifolds. The proof is based on a refined bubbling analysis, for which the main estimates are given in integral form. Our result is used in a subsequent paper to find critical points (via minimax arguments) of some geometric functional, which give rise to conformal metrics of constant Q-cur...

Oscillation of Solutions to Fourth-order Trinomial Delay Differential Equations

The objective of this article is to study the oscillation properties of the solutions to the fourth-order linear trinomial delay differential equation y(t) + p(t)y′(t) + q(t)y(τ(t)) = 0. Applying suitable comparison principles, we present new criteria for oscillation. In contrast with the existing results, we establish oscillation of all solutions, and essentially simplify the examination proce...

Blow up of Solutions for a System of Nonlinear Higher-order Kirchhoff-type Equations

In this work, we consider the initial boundary value problem for the Kirchhoff-type equations with damping and source terms  utt +M (∫ Ω ∣∣∣(−△)m2 u∣∣∣2 dx) (−△) u+ |ut| ut = f1 (u, v) , vtt +M (∫ Ω ∣∣∣(−△)m2 v∣∣∣2 dx) (−△) v + |vt| vt = f2 (u, v) in a bounded domain. We prove the blow up of the solution with positive initial energy by using the technique of [26] with a modification in th...