Let Ω ⊂ RN be a bounded open set with smooth boundary and p = 2N/(N -2) be the critical Sobolev exponent. In this note we extend the results of  and  concerning nodal solutions (i.e., a solution which changes sign) for the Dirichlet problem: -Δu = |u|P-2 u + λu on Ω and u = 0 on ∂Ω, when N ≥ 6 and λ ∈ (0, λ1) with λ1 the first eigenvalue of -Δ. in H10(Ω). Similarly, for the problem -Δu = |u|P-2 u + λ|u|q-2 u on Ω and u = 0 on ∂Ω we obtain a nodal solution when λ > 0, (N + 2)/(N-2) < q < 2N/(N-2) for N = 3, 4, 5 and 2 < q < 2N/(N-2) for N ≥ 6.
|Original language||English (US)|
|Number of pages||18|
|Journal||Differential and Integral Equations|
|State||Published - Jan 1 1992|
All Science Journal Classification (ASJC) codes
- Applied Mathematics