Existence problems for the p-Laplacian

Existence problems for the p-Laplacian

We consider a number of boundary value problems involving the p-Laplacian. The model case is −∆pu = V |u|p−2u for u ∈ W 1,p 0 (D) with D a bounded domain in R. We derive necessary conditions for the existence of nontrivial solutions. These conditions usually involve a lower bound for a product of powers of the norm of V , the measure of D, and a sharp Sobolev constant. In most cases, these ineq...

Existence and uniqueness of solutions for p-laplacian fractional order boundary value problems

In this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-Laplacian fractional order differential equations. We use Schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. We include some examples to show the applicability of our results.

existence and uniqueness of solutions for p-laplacian fractional order boundary value problems

in this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-laplacian fractional order differential equations. we use schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. we include some examples to show the applicability of our results.

Existence Results For Dirichlet Problems With Degenerated p-Laplacian And p-Biharmonic Operators∗

In this article, we prove the existence and uniqueness of solutions for the Dirichlet problem (P ) { ∆(ω(x)|∆u|∆u)− div[ω(x)|∇u|∇u] = f(x)− div(G(x)), in Ω u(x) = 0, in ∂Ω where Ω is a bounded open set of R (N≥2), f∈L (Ω, ω) and G/ω∈[L (Ω, ω)] .

Existence and Uniqueness of Solutions for Boundary Value Problems to the Singular One-Dimension p-Laplacian