In previous work by Castro, Cossio, and Neuberger [2], it was shown that a superlinear Dirichlet problem has at least three nontrivial solutions when the derivative of the nonlinearity at zero is less than the first eigenvalue of with zero Dirichlet boundry condition. One of these solutions changes sign exactly-once and the other two are of one sign. In this paper we show that when this derivative is between the k-th and k +1-st eigenvalues there still exists a solution which changes sign at most k times. In particular, when k = 1 the sign-changing exactly-once solution persists although one-sign solutions no longer exist.

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A sign-changing solution for a superlinear dirichlet problem

Multiplicity Results for Some Nonlinear Elliptic Equations

Exact Multiplicity of Positive Solutions for a Class of Semilinear Problem, II

In this paper we summarize the developments of semipositone problems to date, including very recent results on semipositone systems. We also discuss applications and open problems.

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Nonlinear eigenvalue problems with semipositone structure

Positive Solutions of Quasilinear Boundary Value Problems

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D. Arcoya

Papers

Positive solutions for some semi-positone problems via bifurcation theory