Physical Sciences and Mathematics Commons^™

On Multiple Solutions Of A Nonlinear Dirichlet Problem, Alfonso Castro, Jorge Cossio, John M. Neuberger

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We prove that a semilinear elliptic boundary value problem has five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. We also prove that if the region is a ball the semilinear elliptic problem has two solutions that change sign and are nonradial.