Geodesic
The Lazer-McKenna conjecture for radial solutions in the \(\mathbb R^N\) ball
Electronic journal of differential equations, Tome 1993 (1993) no. 7
When the range of the derivative of the nonlinearity contains the first k eigenvalues of the linear part and a certain parameter is large, we establish the existence of 2k radial solutions to a semilinear boundary value problem. This proves the Lazer McKenna conjecture for radial solutions. Our results supplement those in [5], where the existence of k + 1 solutions was proven.
Classification : 34B15, 35J65
Keywords: lazer-mckenna conjecture, radial solutions, jumping nonlinearities 
@article{EJDE_1993__1993_7_a0,
     author = {Castro,  Alfonso and Gadam,  Sudhasree},
     title = {The {Lazer-McKenna} conjecture for radial solutions in the \(\mathbb {R^N\)} ball},
     journal = {Electronic journal of differential equations},
     year = {1993},
     volume = {1993},
     number = {7},
     zbl = {0810.34016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1993__1993_7_a0/}
}
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Castro,  Alfonso; Gadam,  Sudhasree. The Lazer-McKenna conjecture for radial solutions in the \(\mathbb R^N\) ball. Electronic journal of differential equations, Tome 1993 (1993) no. 7. http://geodesic.mathdoc.fr/item/EJDE_1993__1993_7_a0/