... Equations of Second Order, Springer, Berlin,Germany, 2nd edition, 1993.14 P L. Lions, On positive solutions of semilinear elliptic equations in unbounded domains,” in Nonlinear Diffusion Equations ... S. B. Tshinanga, On multiple solutions of semilinear elliptic equation on unbounded domains withconcave and convex nonlinearities,” Nonlinear Analysis: Theory, Methods & Applications, vol. ... maximum principle for weak solutions see 13, we can show that u1> 0inRN.Proof of Theorem 1.1. Applying Propositions 2.4 and 2.9, we can obtain the conclusion of Theorem 1.1.3. Proof of...