This paper deals with a class of singular semilinear elliptic Dirichlet boundary value problems where the combined effects of a superlinear and a singular term allow us to establish some existence and multiplicity results.
We consider the singular boundary value problem, γ ∈ (0, 1). It is well known that there exists λ * > 0 such that the problem has a solution for all λ ∈ (0, λ * ) and no solution for λ > λ * . We obtain an exact result for λ * (Ω, p, γ, h).
Existence of infinitely many periodic solutions for the 1-dimensional p-Laplacian equationis proved by means of the Poincaré-Birkhoff fixed point theorem, where g ∈ C(R, R) and is p-sublinear at the origin in the sense lim |x|→0 g(x) |x| p−2 x = +∞and f ∈ C(R × R, R) is 1-periodic in the time t, and small with respect to g.
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