On Multiple Solutions For A Class Of Semilinear Ellidtic Equations

In this thesis, we focus on the existence of multiple solutions for the following semilinear elliptic equations where Ω is a smooth bounded domain in RN（N≥3）,λ∈R is a parameter,f and g are locally Lipschitz continuous functions on R satisfying （f1） there exist c0> 0, s₀> 0 such that where. is the first eigenvalue of （-△,H01（Q））;By using a truncation technique and the method of invariant sets of descending flow, we show that （（?）λ） has at least a positive solutions u1, a negative solution u2 and a sign-changing solution u3 for small |λ| and β> 0. Moreover, we also prove that （（?）λ） has has three nontrivial solutions with properties as the preceding in the case that |λ| is small,β=0 and f satisfies an addition conditionWe should emphasize that the function f of the thesis may not satisfy the famous condition （AR）.