Critical Singular Problems on Unbounded Domains

with a continuous function a and a subcritical growth function g. This type of equation includes the Makutuma equation, when a(|x|) = 1/(1 + |x|2) and g(s) = |s|p−1s, with 1 < p < 2∗ − 1 = (N + 2)/(N − 2), which appears in astrophysics and scalar curvature equations on RN (see, e.g., [15, 17, 18]) In [16] Munyamarere and Willem obtained a result of multiplicity of nodal solutions for these equations, considering the function a nonnegative and radially symmetric. The authors worked with a subspace of radial functions ofH1(RN ) which has the compactness properties desired to handle a problem like this modelled on an unbounded domain. In the same direction, Alama and Tarantello [2] studied the following problem when a is not radially symmetric and changes sign (see also [1, 7, 21, 22]):