Oscillating minimizers of a fourth-order problem invariant under scaling

N ov 2 00 3 Oscillating minimizers of a fourth order problem invariant under scaling ∗ †

By variational methods, we prove the inequality ∫

On a Fourth Order Curvature Invariant

Approximate solution of fourth order differential equation in Neumann problem

Generalized solution on Neumann problem of the fourth order ordinary differential equation in space $W^2_alpha(0,b)$ has been discussed, we obtain the condition on B.V.P when the solution is in classical form. Formulation of Quintic Spline Function has been derived and the consistency relations are given.Numerical method,based on Quintic spline approximation has been developed. Spline solution ...

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...

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.