Existence And Nonexistence Of Positive Solutions For Nonhomogeneous Semilinear Elliptic Equations

We consider the existence and nonexistence of positive solutions for the following Qonhomogeneoussexnilinear. elliptic problemwhere is a bounded domain, , for N > 2, and ,for satisfies the following condition(H) , and the linear mixed boundary value problemhas nonegative solution .In the discussion of the existence of positive solutions of the problem (1), assumption (H) is weaker than the assumption f(x) > 0 in the most of references. Since f(x) is permitted to change sign under the assumption (H).The main tools used in this paper are sub-supsolution principle, variations! approach, mountain pass lemma, etc. The main result obtained in this paper is as follows:Theorem Assume that f(x) satisfies (H) and that 2 then, there exists two positive numbers such that the problem (1) has at least two positive solutions for while has no positive solution for...