A new and extended variational characterization of the Fucik Spectrum with application to nonresonance and resonance problems

作者：Drabek Pavel; Robinson Stephen B.^*

来源：Calculus of Variations and Partial Differential Equations, 2018, 57(1): 1.

DOI：10.1007/s00526-017-1276-8

We consider the boundary value problem
-Delta u = alpha u(+) - beta u(-) in Omega,
u = 0 on partial derivative Omega,
where Omega is a smooth bounded domain in R-N, u(+/-) := max{+/- u, 0}, and (alpha, beta) is an element of R-2. When this problem has a nontrivial solution, then (alpha, beta) is an element of the Fucik Spectrum, Sigma. Ourmain result is to extend the variational characterization, due to Castro and Chang in 2010, of several curves in Sigma. As an application we prove existence theorems for nonresonance and resonance problems relative to these extended spectral curves.

• 出版日期2018-2