Semilinear elliptic equations and nonlinearities with zeros

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• 作者：Begoñ ; a Barrios^a ; ^{bego.barrios@uam.es" class="auth_mail" title="E-mail the corresponding author} ; Jorge Garcí ; a-Meliá ; n^b ; ^c ; ^{jjgarmel@ull.es" class="auth_mail" title="E-mail the corresponding author} ; Leonelo Iturriaga^d ; ^{leonelo.iturriaga@usm.cl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 35J25 ; 35J61 ; secondary ; 49J35 ; 35A15
• 刊名：Nonlinear Analysis
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：134
• 期：Complete
• 页码：117-126
• 全文大小：555 K

文摘

In this paper we consider the semilinear elliptic problem where f$f$ is a nonnegative, locally Lipschitz continuous function, Ω$\Omega$ is a smooth bounded domain and 15e2e7" title="Click to view the MathML source">λ>0$\lambda >0$ is a parameter. Under the assumption that f$f$ has an isolated positive zero α$\alpha$ such that for some small δ>0$\delta >0$, we show that for large enough λ$\lambda$ there exist at least two positive solutions u_λ<v_λ$u_{\lambda }<v_{\lambda }$, verifying ‖u_λ‖_∞<α<‖v_λ‖_∞${\Vert u_{\lambda }\Vert }_{\infty }<\alpha <{\Vert v_{\lambda }\Vert }_{\infty }$ and u_λ,v_λ→α$u_{\lambda },v_{\lambda }\to \alpha$ uniformly on compact subsets of Ω$\Omega$ as λ→+∞$\lambda \to +\infty$. The existence of these solutions holds independently of the behavior of f$f$ near zero or infinity.