논문 해외 국제전문학술지(SCI급) Infinite multiplicity of stable entire solutions for a semilinear elliptic equation with exponential nonlinearity
- 학술지 구분 국제전문학술지(SCI급)
- 게재년월 2019-10
- 저자명 배수현
- 학술지명 PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
- 발행처명 CAMBRIDGE UNIV PRESS
- 발행국가 해외
- 논문언어 외국어
- 전체저자수 1
홈페이지논문 초록 (Abstract)
We consider the infinite multiplicity of entire solutions for the elliptic equation Delta u + K(x)e(u) + mu f(x) = 0 in Double-struck capital R-n, n > 3. Under suitable conditions on K and f, the equation with small mu > 0 possesses a continuum of entire solutions with a specific asymptotic behaviour. Typically, K behaves like |x|(l) at infinity for some l > -2 and the entire solutions behave asymptotically like - (2 + l)log |x| near infinity. Main tools of the analysis are comparison principle for separation structure, asymptotic expansion of solutions near infinity, barrier method and strong maximum principle. The linearized operator for the equation has two characteristic behaviours related with the stability and the weak asymptotic stability of the solutions as steady states for the corresponding parabolic equation.