Exact multiplicity results for a p-Laplacian problem with concave–convex–concave nonlinearities

Exact multiplicity results for a class of two-point boundary value problems

“…The problem (1.1) arises in many different situations. Some results have been obtained under different assumptions on f and p, for instance, see [1][2][3][4][5][9][10][11][12][15][16][17][18].…”

Existence and multiplicity results for a class of p-Laplacian problems with Neumann–Robin boundary conditions

“…is the positone problem), and we shall assume that f 0 (s) P 0, f 00 (s) > 0, lim s !1 writing). In [1] the problem (1) with Dirichlet boundary has been studied by using quadrature method. In [3,4], (1) in the case p = 2 has been studied when a < 0 and a > 0, respectively, and for semipositone problems, existence and multiplicity results have been established for the case a = 0 in [5] also in [2] have been studied nonnegative solution curves with Dirichlet boundary for semipositone problems.…”

“…In [1] the problem (1) with Dirichlet boundary has been studied by using quadrature method. In [3,4], (1) in the case p = 2 has been studied when a < 0 and a > 0, respectively, and for semipositone problems, existence and multiplicity results have been established for the case a = 0 in [5] also in [2] have been studied nonnegative solution curves with Dirichlet boundary for semipositone problems. Also other types of two point boundary value problems of (1) in the case p = 2 have been studied in [6][7][8].…”

Uniqueness results for the one-dimensional p-Laplacian

“…When f is a C 2 function and convex or concave, the exact number of positive solutions was studied by many authors; see for instance [1,3,5,6].…”

“…1) where C p and Λ are given by (1.3) and (1.6)-(1.8).For r ∈ Λ, let u(r, t) be a unique solution of the problem:0 u(t) r, = |t|,(2.2)for t ∈ [−T (r), T (r)].Remark 2.1. For r > η, by (A1) and (1.5) we have f (r) > 0 andr v f (z) dz > 0 for 0 v < r. Thus, T (r) is well defined for all r ∈ Λ.…”