Existence of Sign-Changing Solutions to Equations Involving the One-Dimensional p-Laplacian

Abstract EN

We consider the equations involving the one-dimensional p-Laplacian (P): (u′tp-2u′(t))′+λf(u(t))=0, 01,λ>0,f∈C1(R;R),f(s)s>0, and s≠0.

We show the existence of sign-changing solutions under the assumptions f∞=lim|s|→∞(fs/sp-1)=+∞ and f0=lim|s|→0(f(s)/sp-1)∈[0,∞].

We also show that (P) has exactly one solution having specified nodal properties for λ∈(0,λ*) for some λ*∈(0,∞).

Our main results are based on quadrature method.