The existence, uniqueness and asymptotic behavior of positive solutions of the semilinear elliptic equations with asymptotic linear nonlinearity was studied. It was proved that if ε > 0, then there existed exactly one solution uλ(.,ε) for all λ ∈ (0,λ1) where λ1 represents first eignvalue of -δ in ω with Dirichlet boundary condition. The results showed that if s < t and small enough, δū+λfε(ū) < -s + ||h(ū)||∞ ≤ 0 was found by choosing δ = s.
|Number of pages||9|
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|State||Published - Jul 2002|
- Hopf lemma
- Minimal solution
- Perturbation lemma
- Variation method of Nehari-type