Remarks on Lévy's Fourth Order Potential

Remarks on solutions of a fourth-order problem

In this paper, we study the two following minimization problems: S0(q, φ) = inf u∈H2 0 (Ω),‖u+φ‖q=1 ∫ Ω | u|2 and Sθ (q, φ) = inf u∈H2 θ (Ω),‖u+φ‖q=1 ∫ Ω | u|2. We prove that for a class of maps φ, we have Sθ (q, φ) < S0(q, φ) and for another class, we have Sθ (q, φ) = S0(q, φ). c © 2005 Elsevier Ltd. All rights reserved.

Remarks on entire solutions for two fourth order elliptic problems

We are interested in entire solutions for the semilinear biharmonic equation ∆u = f(u) in R , where f(u) = e or −u−p (p > 0). For the exponential case, we prove that for the polyharmonic problem ∆u = e with positive integer m, any classical entire solution verifies ∆2m−1u < 0, this completes the results in [6, 14]; we obtain also a refined asymptotic expansion of radial separatrix solution to ∆...

Fourth order and fourth sum connectivity indices of tetrathiafulvalene dendrimers

The m-order connectivity index (G) m of a graph G is     1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i m d d d  G where 1 2 1 ... i i im d d d  runs over all paths of length m in G and i d denotes the degree of vertex i v . Also,        1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i ms d d d X G is its m-sum connectivity index. A dendrimer is an artificially manufactured or synth...

On a Fourth Order Curvature Invariant

Fourth-order Operators on Manifolds with Boundary

Recent work in the literature has studied fourth-order elliptic operators on manifolds with boundary. This paper proves that, in the case of the squared Laplace operator, the boundary conditions which require that the eigenfunctions and their normal derivative should vanish at the boundary lead to self-adjointness of the boundary-value problem. On studying, for simplicity, the squared Laplace o...