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Article Contents

Precise range of the existence of positive solutions of a nonlinear, indefinite in sign Neumann problem

• We study positive solutions of an elliptic problem with indefinite in sign nonlinear Neumann boundary condition that depends on a real parameter, $\lambda$. We find precise range, $I$, of those $\lambda$'s for which our problem possesses a positive solution, prove that $\lambda^$∗ = sup $I$ is a bifurcation point, and exhibit explicit max-min procedure for computing $\lambda^$∗. We also obtain some properties of the set of solutions.
Mathematics Subject Classification: Primary: 35J65, 35P30; Secondary: 35J20.

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