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

[摘要] We consider the equations involving the one-dimensionalp-Laplacian(P):  (u′tp-2u′(t))′+λf(u(t))=0,01,λ>0,f∈C1(R;R),f(s)s>0,ands≠0. We show the existence of sign-changing solutions under the assumptionsf∞=lim|s|→∞⁡(fs/sp-1)=+∞andf0=lim|s|→0(f(s)/sp-1)∈[0,∞]. We also show that(P)has exactly one solution having specified nodal properties forλ∈(0,λ*)for someλ*∈(0,∞). Our main results are based on quadrature method.

[学科分类] 应用数学