Abstract:
In this article, we study the existence and multiplicity of nontrivial solutions
to the problem
−
2F(x, D2u) = f(x, u) + ψ(Du) in Ω,
u = 0 on ∂Ω,
where Ω is a smooth bounded domain in R
n, n > 2. We show that the problem
possesses nontrivial solutions for small value of provided f and ψ are continuous and
f has a positive zero. We employ degree theory arguments and Liouville type theorem
for the multiplicity of the solutions.