www.heavensgatel2.fora.pl

[px919557]

A Class of Indefinite Quasilinear Elliptic Equations


A M; Also, according to , (u,), one can get ul 』 uF (, u,) ≤ IIuII, 』 II A (X, Um, VmIIII, 10JIIII: +0 IIuII +0 IIII a M,, then , (u, ) Is a bounded sequence. and then there is strong convergence of sub- column card . According to the conditions (H to get F (, u,) satisfy the sub-critical growth, by the Sobolev embedding theorem , () CL (),() CL () is Compact embedding , since (u,) is a bounded sequence , then (u,) has a strong convergence of sub- columns. Theorem 2.1 assumptions (H) ~ (H) was established , and m (), n () satisfy the type (1.1 ) and ( 1.2) , when A ∈ (0, A.), ∈ (0,.) , the problem (P) there is non- trivial solution . A , I__,[link widoczny dla zalogowanych], A - l, J - _ a P, ≥ 1 of this chapter by C Day , et al: A Class of Indefinite Quasilinear Elliptic Equations Proof: From Lemma 2.2_ mouth ] obtained functional (U,) satisfy (PS) condition , F surface proved functional (U,) satisfy the conditions of Lemma 2.1 (1 ), ( 2) ( ie J, (By the condition (H) available, (0,0 ) = 0 , then according to condition (H, (H) and the Sobolev embedding theorem we know that there is P 0, P> 0, such that llu + = p sufficiently small, there is , (u ,)>£> 0. (2) , according to the conditions (H,) can be obtained There dock > o, P 1, + q <1 ~ t.Op + Oq'y2 ≥ 1. After a simple calculation , obviously available , functional F (, u,) satisfies the condition ( H) A (H).