Invariant criteria for existence of bounded positive solutions
نویسندگان
چکیده
We consider semilinear elliptic equations ∆u ± ρ(x)f(u) = 0, or more generally ∆u + φ(x, u) = 0, posed in RN (N ≥ 3). We prove that the existence of bounded positive entire solutions is closely related to the existence of bounded solution for ∆u + ρ(x) = 0 in RN . Many sufficient conditions which are invariant under the isometry group of RN are established. Our proofs use the standard barrier method, but our results extend many earlier works in this direction. Our ideas can also be applied for the existence of large solutions and for the system cases. 2000 MSC: 35J60, 35B05, 35B50, 35B35
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