Asymptotically Linear Problems and Antimaximum Principle for the Square Root of the Laplacian

作者：Arcoya David^*; Colorado Eduardo; Leonori Tommaso

来源：Advanced Nonlinear Studies, 2012, 12(4): 683-701.

DOI：10.1515/ans-2012-0402文章关键词:fractional laplacian,nonlinear problem,bifurcation,antimaximum principle原

• fractional laplacian
• nonlinear problem
• bifurcation
• antimaximum principle

This work deals with bifurcation of positive solutions for some asymptotically linear problems, involving the square root of the Laplacian (-Delta)(1/2). A simplified model problem is the following: %26lt;br%26gt;{(-Delta)(1/2)u = lambda m(x)u + g(u) in Omega, u = 0 on partial derivative Omega, %26lt;br%26gt;with Omega subset of R-N a smooth bounded domain, N %26gt;= 2, lambda %26gt; 0, m is an element of L-infinity(Omega), m(+) not equivalent to 0 and g is a continuous function which is super-linear at 0 and sub-linear at infinity. As a consequence of our bifurcation theory approach we prove some existence and multiplicity results. Finally, we also show an anti-maximum principle in the corresponding functional setting.

• 出版日期2012-11