... α∞0Ω,respectively.The existence of ground state solutions of Eb is affected by the shape of the domainΩ and bx that satisfies some suitable conditions and has been the focus of a great deal of research in ... ∈M−λa,bΩ ,and Jλa,btu inf0≤t≤tmaxuJλa,btu,Jλa,bt−u supt≥0Jλa,btu.2.17Proof. TheproofisalmostthesameasthatinWu32, Lemma 5 andisomittedhere.3. Proof of ... Journal of Mathematical Analysis and Applications, vol. 318, no. 1, pp. 253–270, 2006.33 H. Br´ezis and E. Lieb, “A relation between pointwise convergence of functions and convergence of functionals,”...