We consider a (p,2)-equation
with a Carathéodory reaction f(z,x) which is resonant at ±∞ and has constant
sign, z-dependent zeros. Using variational methods, together with truncation and
comparison techniques and Morse theory, we establish the existence of five nontrivial
smooth solutions (four of constant sign and the fifth nodal). If the reaction f(z,x) is
C1 in x ∈ ℝ, then we produce a second nodal solution for a total of six nontrivial
smooth solutions.
Keywords
resonant equations, tangency principle, strong comparison
principle, constant sign and nodal solutions, Morse theory