Arcoya, DavidColorado, EduardoLeonori, Tommaso2024-11-212024-11-212016-03-10Arcoya, David, Colorado, Eduardo and Leonori, Tommaso. "Asymptotically Linear Problems and Antimaximum Principle for the Square Root of the Laplacian" Advanced Nonlinear Studies, vol. 12, no. 4, 2012, pp. 683-701. https://doi.org/10.1515/ans-2012-04022169-0375https://doi.org/10.1515/ans-2012-0402https://hdl.handle.net/20.500.14468/24463Dedicato ad Antonio Ambrosetti in occasione del suo pensionamento dalla SISSAThis 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: {(-Delta)(1/2)u = lambda m(x)u + g(u) in Omega, u = 0 on partial derivative Omega, with Omega subset of R-N a smooth bounded domain, N >= 2, lambda > 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.eninfo:eu-repo/semantics/openAccess12 Matemáticasartículofractional laplaciannonlinear problembifurcationantimaximum principle