
Eigenvalue problem for fully nonlinear secondorder elliptic PDE on balls, IIEigenvalue problem for fully nonlinear secondorder elliptic PDE on balls, IIAA12536502 
"/Ikoma, Norihisa(1000050728342)/"Ikoma, Norihisa ,
"/Ishii, Hitoshi/"Ishii, Hitoshi
5
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3
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, pp.451

510 , 20151001 , Springer Open
ISSN:16643615
NCID:AA12536502
Description
This is a continuation of Ikoma and Ishii (Ann Inst H Poincaré Anal Non Linéaire 29:783–812, 2012) and we study the eigenvalue problem for fully nonlinear elliptic operators, positively homogeneous of degree one, on finite intervals or balls. In the multidimensional case, we consider only radial eigenpairs. Our eigenvalue problem has a general firstorder boundary condition which includes, as a special case, the Dirichlet, Neumann and Robin boundary conditions. Given a nonnegative integer n, we prove the existence and uniqueness, modulo multiplication of the eigenfunction by a positive constant, of an eigenpair whose eigenfunction, as a radial function in the multidimensional case, has exactly n zeroes. When an eigenfunction has n zeroes, we call the corresponding eigenvalue of nth order. Furthermore, we establish results concerning comparison of two eigenvalues, characterizations of nth order eigenvalues via differential inequalities, the maximum principle for the boundary value problem in connection with the principal eigenvalue, and existence of a solution having n zeroes, as a radial function in the multidimensional case, of the boundary value problem with an inhomogeneous term. © 2015, The Author(s).
FullText
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