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The Lazer-McKenna conjecture for radial solutions in the \(\mathbb R^N\) ball. (English) Zbl 0810.34016

Summary: 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 of D. G. Costa and D. G. de Figueiredo [J. Differ. Equations 60, 80–89 (1985; Zbl 0566.35049)], where the existence of \(k+1\) solutions was proven.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
35J65 Nonlinear boundary value problems for linear elliptic equations

Citations:

Zbl 0566.35049
Full Text: EuDML EMIS