AbstractWe prove new existence results for a nonlinear Helmholtz equation with sign-changing nonlinearity of the form $$\begin{aligned} - \Delta u - k^{2}u = Q(x)|u|^{p-2}u, \quad u \in W^{2,p}\left( {\mathbb {R}}^{N}\right) \end{aligned}$$
-
Δ
u
-
k
2
u
=
Q
(
x
)
|
u
|
p
-
2
u
,
u
∈
W
2
,
p
R
N
with $$k>0,$$
k
>
0
,
$$N \ge 3$$
N
≥
3
, $$p \in \left[ \left. \frac{2(N+1)}{N-1},\frac{2N}{N-2}\right) \right. $$
p
∈
2
(
N
+
1
)
N
-
1
,
2
N
N
-
2
and $$Q \in L^{\infty }({\mathbb {R}}^{N})$$
Q
∈
L
∞
(
R
N
)
. Due to the sign-changes of Q, our solutions have infinite Morse-Index in the corresponding dual variational formulation.