Multiple Solutions of a Nonlinear Biharmonic Equation on Graphs

Existence of Positive Solutions to a Nonlinear Biharmonic Equation

In this note we use the Nehari manifold and fibering maps to show existence of positive solutions for a nonlinear biharmonic equation in a bounded smooth domain in Rn, when n = 5, 6, 7. Mathematics Subject Classification: 35J35, 35J40

Existence of Multiple Solutions for a Quasilinear Biharmonic Equation

Using three critical points theorems, we prove the existence of at least three solutions for a quasilinear biharmonic equation.

EXISTENCE OF MULTIPLE SOLUTIONS FOR A p(x)-BIHARMONIC EQUATION

In this article, we show the existence of at least three solutions to a Navier boundary problem involving the p(x)-biharmonic operator. The technical approach is mainly base on a three critical points theorem by Ricceri.

Ring-type singular solutions of the biharmonic nonlinear Schrödinger equation

We present new singular solutions of the biharmonic nonlinear Schrödinger equation (NLS) iψt(t,x)− ψ + |ψ |2σψ = 0, x ∈ R , 4/d σ 4. These solutions collapse with the quasi-self-similar ring profile ψQB , where |ψQB(t, r)| ∼ 1 L2/σ (t) QB ( r − rmax(t) L(t) ) , r = |x|, L(t) is the ring width that vanishes at singularity, rmax(t) ∼ r0L(t) is the ring radius, and α = (4 − σ)/(σ (d − 1)). The blo...

On Univalent Solutions of the Biharmonic Equation