Multiple positive solutions of singular and critical elliptic problem in with discontinuous nonlinearities

作者：Sreenadh K^*; Tiwari Sweta

来源：Nodea-Nonlinear Differential Equations and Applications, 2013, 20(6): 1831-1850.

DOI：10.1007/s00030-013-0232-3

• Singular elliptic problem
• Critical growth
• Discontinuous nonlinearity

Let Omega be a bounded domain in with smooth boundary. We consider the following singular and critical elliptic problem with discontinuous nonlinearity: %26lt;br%26gt;(P-lambda) {-Delta u = lambda(m(x,u)e(alpha u2)/vertical bar x vertical bar(beta) + u(q)g(u - a)), u %26gt; 0 in Omega %26lt;br%26gt;u = 0 on partial derivative Omega %26lt;br%26gt;where 0 %26lt;= q %26lt; 1, 0 %26lt; alpha %26lt;= 4 pi and beta is an element of [0, 2) such that beta/2 + alpha/4 pi %26lt;= 1 and g(t - a) - {(1, t %26lt;= a)(0, t %26gt; a). Under the suitable assumptions on m(x, t) we show the existence and multiplicity of solutions for maximal interval for lambda.

• 出版日期2013-12