BOUNDARY ESTIMATES FOR SOLUTIONS OF WEIGHTED SEMILINEAR ELLIPTIC EQUATIONS

作者：Anedda Claudia^*; Porru Giovanni

来源：Discrete and Continuous Dynamical Systems, 2012, 32(11): 3801-3817.

DOI：10.3934/dcds.2012.32.3801

• Singular elliptic equations
• blow-up solutions
• boundary estimates
• weighted equations
• second order estimates

Let b(x) be a positive function in a bounded smooth domain Omega subset of R-N, and let f(t) be a positive non decreasing function on (0, infinity) such that lim(t -%26gt;infinity) f (t) = infinity. We investigate boundary blow-up solutions of the equation Delta u = b(x)f(u). Under appropriate conditions on b(x) as x approaches partial derivative Omega and on f(t) as t goes to infinity, we find a second order approximation of the solution u(x) as x goes to partial derivative Omega. %26lt;br%26gt;We also investigate positive solutions of the equation Delta u+(delta(x))(2l)u(-q) = 0 in Omega with u = 0 on partial derivative Omega, where l %26gt;= 0, q %26gt; 3 + 2l and delta(x) denotes the distance from x to partial derivative Omega. We find a second order approximation of the solution u(x) as x goes to partial derivative Omega.

• 出版日期2012-11