Using a combination of several methods, such as variational methods, the sub and supersolutions method, comparison principles and a priori estimates, we study existence, multiplicity, and the behavior with respect to λ of positive solutions of p-Laplace equations of the form - Δpu = λ h (x, u), where the nonlinear term has p-superlinear growth at infinity, is nonnegative, and satisfies h (x, a (x)) = 0 for a suitable positive function a. In order to manage the asymptotic behavior of the solutions we extend a result due to Redheffer and we establish a new Liouville-type theorem for the p-Laplacian operator, where the nonlinearity involved is superlinear, nonnegative, and has positive zeros. © 2009 Elsevier Inc. All rights reserved.
Iturriaga, L., Massa, E., Sánchez, J., & Ubilla, P. (2010). Positive solutions of the p-Laplacian involving a superlinear nonlinearity with zeros. Journal of Differential Equations, 309-327. https://doi.org/10.1016/j.jde.2009.08.008