Boundary value problems for quasilinear differential equations appear in many mathematical models nowadays. Solvability and dependence of the number of solutions on parameters is often asked by the people from praxis. A prototype of such a problem is the Dirichlet problem for the so-called p-Laplacian:
- div(|grad u|(p-2) grad u) - λ |u|(p-2)u + g(λ], x, u)= f , in Ω u=0, on ∂Ω
As theoretical works show, solvability of this problem is closely related to the following nonlinear eigenvalue problem:
(|u'|(p-2)u')' - λ |u|(p-2)u = 0, in (0,1); u(0)=0, u(1)=0
Very little is known about higher eigenvalues of this problem. For that reason, we have decided to study this problem with the aid of numerical experiments to get some idea what we can expect.