Non uniqueness for the Dirichlet problem for fully nonlinear elliptic operators and the Ambrosetti-Prodi phenomenon
Sirakov, Boyan
HAL, hal-00079186 / Harvested from HAL
Text on HAL
We study the uniformly elliptic fully nonlinear PDE F (D 2 u, Du, u, x) = f (x) in Ω, where F is a convex positively 1-homogeneous operator and Ω ⊂ R N is a regular bounded domain. We prove non-existence and multiplicity results for the Dirichlet problem, when the two principal eigenvalues of F are of different sign. Our results extend to more general cases, for instance, when F is not convex, and explain in a new light the classical results of Ambrosetti-Prodi type in elliptic PDE.
Publié le : 2012-09-17
Classification:  [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 
@article{hal-00079186,
     author = {Sirakov, Boyan},
     title = {Non uniqueness for the Dirichlet problem for fully nonlinear elliptic operators and the Ambrosetti-Prodi phenomenon},
     journal = {HAL},
     volume = {2012},
     number = {0},
     year = {2012},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00079186}
}

Sirakov, Boyan. Non uniqueness for the Dirichlet problem for fully nonlinear elliptic operators and the Ambrosetti-Prodi phenomenon. HAL, Tome 2012 (2012) no. 0, . http://gdmltest.u-ga.fr/item/hal-00079186/