Eigenvalue problem for p-Laplacian with mixed boundary conditions

Existence solutions for new p-Laplacian fractional boundary value problem with impulsive effects

Fractional differential equations have been of great interest recently. This is because of both the intensive development of the theory of fractional calculus itself and the applications of such constructions in various scientific fields such as physics, mechanics, chemistry, engineering, etc. Differential equations with impulsive effects arising from the real world describe the dyn...

THE FIRST EIGENVALUE OF p-LAPLACIAN SYSTEMS WITH NONLINEAR BOUNDARY CONDITIONS

Inverse nodal problem for p-Laplacian with two potential functions

In this study, inverse nodal problem is solved for the p-Laplacian operator with two potential functions. We present some asymptotic formulas which have been proved in [17,18] for the eigenvalues, nodal points and nodal lengths, provided that a potential function is unknown. Then, using the nodal points we reconstruct the potential function and its derivatives. We also introduce a solution of i...

A generalized Fucik type eigenvalue problem for p-Laplacian

In this paper we study the generalized Fucik type eigenvalue for the boundary value problem of one dimensional p−Laplace type differential equations { −(φ(u′))′ = ψ(u), −T < x < T ; u(−T ) = 0, u(T ) = 0 (∗) where φ(s) = αs + − βs − , ψ(s) = λs + − μs − , p > 1. We obtain a explicit characterization of Fucik spectrum (α, β, λ, μ), i.e., for which the (*) has a nontrivial solution. (1991) AMS Su...

THE EIGENVALUE PROBLEM FOR THE p-LAPLACIAN-LIKE EQUATIONS

We consider the eigenvalue problem for the following p-Laplacian-like equation: −div(a(|Du| p)|Du| p−2 Du) = λf (x, u) in Ω, u = 0 on ∂Ω, where Ω ⊂ R n is a bounded smooth domain. When λ is small enough, a multiplicity result for eigen-functions are obtained. Two examples from nonlinear quantized mechanics and capillary phenomena, respectively, are given for applications of the theorems.