Generalized quasilinear Schrödinger equations with critical growth

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• 作者：Yongkuan Cheng ; ^{chengyk@scut.edu.cn} ; Yaotian Shen ^{maytshen@scut.edu.cn}
• 关键词：Quasilinear Schrö ; dinger equations ; Mountain Pass Theorem ; Critical growth
• 刊名：Applied Mathematics Letters
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：65
• 期：Complete
• 页码：106-112
• 全文大小：777 K
• 卷排序：65

文摘

We establish the existence of nontrivial solutions for the following quasilinear Schrödinger equation: −Δu+V(x)u−Δ[l(u2)]l′(u2)u=uα2∗−1+f(u),x∈RN,where V(x):RN→RV(x):RN→R is a given potential and l,fl,f are real functions, 2∗=2N∕(N−2)2∗=2N∕(N−2), N≥3N≥3. Our results cover two physical models l(s)=sα2, l(s)=(1+s)α2, α>1α>1 and recent results from the literature (Shen and Wang, 2016, Deng et al., 2016) are improved and extended.