We study the relationship between
s and the number of solutions of the second-order Neumann boundary value problem
where
f∈
C([0,1]×
R2,
R),
s∈
R is a parameter. By using the method of the upper and lower solutions and topological degree techniques, we obtain that the problem has no solution, at least one solution and at least two solutions, when
s<
s1,
s=
s1,
s>
s1, respectively.