Existence of positive solutions for a semipositone p-Laplacian problem

Abstract

We prove the existence of positive solutions to a semipositone p-Laplacian problem combining mountain pass arguments, comparison principles, regularity principles and a priori estimates.

Existence of positive radial solutions for a superlinear semipositone p-Laplacian problem on the exterior of a ball

“…In the p-Laplacian case (when p = 2), the help of a Green function is unavailable, which necessitates a deeper analysis. Extending recent ideas from [11] to the case of boundary-value problems with singular weights as well as to boundary-value problems with nonlinear boundary conditions, we establish our results in this paper. In § 2 we recall the mountain pass theorem and an important property (the (S + ) property) of the p-Laplacian operator.…”

Existence of Positive Solution to Schrödinger-type Semipositone Problems with Mixed Nonlinear Boundary Conditions

“…For the case (f ∞ ), the scaling method combined with the degree theory [13] and the mountain pass lemma with C 1,α (Ω)-regularity [9,35] are frequently used to demonstrate the existence of a positive solution for semipositone Laplacian (or p-Laplacian) problems with Dirichlet boundary conditions. Here, more precise assumptions are given for this case.…”

Existence of positive solutions for a class of semipositone problem in whole ℝN

“…The present work has been mainly motivated by papers [7,10], and by the fact that the authors did not find in the literature any paper involving semipositone problem in whole R N by using variational methods. In [7], Caldwell, Castro, Shivaji and Unsurangsie have studied the existence positive solutions for the following class of semipositone problem…”

“…In the literature we find different methods to prove the existence and non existence of solutions, such as sub-supersolutions, degree theory arguments, fixed point theory and bifurcation, see for example the [1,2,5,6] and their references. Besides these methods, the variational method was also used in some few papers as can be seen in [3,7,8,[10][11][12][13][14].…”