Multiple non-trivial solutions of the Neumann problem for p-Laplacian systems
We obtain multiple non-trivial solutions of the Neumann problem for p-Laplacian systems using Morse theory.
Infinitely Many Solutions of The Neumann Problem for Elliptic Equations Involving The p‐Laplacian
In this paper, we prove the existence of an unbounded sequence of weak solutions under an appropriate oscillating behaviour of ϕ for a Neumann problem of the type {div(∣∇u∣p−2∇u)+λ(x)∣u∣p−2u=ϕ(x,u)inΩ∂u/∂v=0on∂Ω.
On Hilbert's thirteenth problem and related questions
Hilbert's thirteenth problem involves the study of solutions of algebraic equations. The object is to obtain a complexity estimate for an algebraic function. As of now, the problem remains open. There are only a few partial algebraic results in this connection, but at the same time the problem has stimulated a series of studies in the theory of functions with their subsequent applications. The most brilliant result in this cycle is Kolmogorov's theorem on superpositions of continuous functions.