Low Perturbations and Combined Effects of Critical and Singular Nonlinearities in Kirchhoff Problems.

In this paper, we study three-dimensional Kirchhoff equations with critical growth and singular nonlinearity. We are concerned with the qualitative analysis of solutions to the following nonlocal problem - a + b ∫ Ω | ∇ u | 2 d x Δ u = λ u - γ + u 5 , in Ω , u > 0 , in Ω , u = 0 , on ∂ Ω , where Ω ⊂ R 3 is a bounded domain with smooth boundary, 0 < γ < 1 , and a , b , λ are positive constants. By combining variational methods with some delicate decomposition techniques, we obtain the existence of two positive solutions in the case of low perturbations of the singular nonlinearity, namely for small values of the parameter λ . [ABSTRACT FROM AUTHOR]