A singularly perturbed nonlinear Robin problem in a periodically perforated domain: a functional analytic approach dagger

作者：de Cristoforis Massimo Lanza^*; Musolino Paolo

来源：Complex Variables and Elliptic Equations, 2013, 58(4): 511-536.

DOI：10.1080/17476933.2011.638716

• periodic nonlinear Robin boundary-value problem
• singularly perturbed domain
• singularly perturbed data
• Laplace operator
• real-analytic continuation in Banach space

Let nN\{0,1}. Let q be the nxn diagonal matrix with entries q 11,...,q nn in] 0, +[. Then qZ n is a q-periodic lattice in n with fundamental cell . Let pQ. Let be a bounded open subset of n containing 0. Let G be a (nonlinear) map from x to . Let be a positive-valued function defined on a right neighbourhood of 0 in the real line. Then we consider the problem for epsilon%26gt;0 small, where p+epsilon denotes the outward unit normal to p+epsilon. Under suitable assumptions and under condition lim epsilon 0+(epsilon)1 epsilon, we prove that the above problem has a family of solutions {u(epsilon, center dot)}epsilon]0, epsilon[ for epsilon sufficiently small, and we analyse the behaviour of such a family as epsilon approaches 0 by an approach which is alternative to those of asymptotic analysis.

• 出版日期2013-4-1