The following boundary value problem(1.1)(φp (u′))′ + a (x) f (u) = 0, x0 < x < x1,(1.2)u (x0) = u (x1) = 0, is considered, where φp (s) = | s |p - 2 s, p > 1, a ∈ C1 [x0, x1], a (x) > 0 for x ∈ [x0, x1], and f ∈ C1 (R). An identity for solutions of (1.1) and its linearized equation is derived. Some applications of the identity to uniqueness of solutions of problem (1.1)-(1.2) are presented. Non-uniqueness examples for problem (1.1)-(1.2) are also established. Moreover the results obtained here are applied to the study of radially symmetric solutions of the Dirichlet problem for elliptic equations in annular domains.
- Quasilinear equation
- Two-point boundary value problem
ASJC Scopus subject areas
- Applied Mathematics