Positive solutions of the p-Laplacian involving a superlinear nonlinearity with zeros

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 lambda of positive solutions of p-Laplace equations of the form -Delta(p)u = lambda 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. (C) 2009 Elsevier Inc. All rights reserved.

FONDECYT[Ndegrees 11080203]

Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) - Chile

Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) - Chile

FONDECYT[1080430]

Convenio de desempeno UTA-MECESUP

Convenio de desempeno UTA-MECESUP[2]

Fapesp

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

CNPq/Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)