On Semipositone Non-Local Boundary-Value Problems with Nonlinear or Affine Boundary Conditions

Abstract

AbstractWe consider the boundary-value problemwhereH: [0,+∞) → ℝ andf: [0, 1] × ℝ → ℝ are continuous and λ > 0 is a parameter. We show that ifHsatisfies a boundedness condition on a specified compact set, then this, together with an assumption thatHis either affine or superlinear at +∞, implies existence of at least one positive solution to the problem, even in the case where we impose no growth conditions onf. Finally, since it can hold thatf(t, y) < 0 for all (t, y) ∈ [0, 1]×ℝ, the semipositone problem is included as a special case of the existence result.