THREE SOLUTIONS FOR A CLASS OF GRADIENT KIRCHHOFF-TYPE SYSTEMS DEPENDING ON TWO PARAMETERS

In this paper we shall discuss the existence of at least three solutions for the class of two-point boundary value Kirchhoff-type systems

( −Ki( Rb a |u ′ i (x)| 2dx)u ′′ i = λFui (x, u1, . . . , un) + µGui (x, u1, . . . , un), ui(a) = ui(b) = 0

for 1 ≤ i ≤ n. The approach is fully based on a recent three critical points theorem of B. Ricceri [A three critical points theorem revisited, Nonlinear Anal. 70/9 (2009) 3084–3089]