A class of semipositonep-Laplacian problems with a critical growth reaction term

Abstract

We prove the existence of ground state positive solutions for a class of semipositone p-Laplacian problems with a critical growth reaction term. The proofs are established by obtaining crucial uniform C1,α a priori estimates and by concentration compactness arguments. Our results are new even in the semilinear case p = 2.

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.…”

Robust numerical method for singularly perturbed differential equations having both large and small delay

“…In this paper, we consider a new governing problem having both small delay on convection term and large delay. Additionally, in recent years the correlative physical phenomena in-depth of the problem under consideration have been done by the authors [13][14][15][16][17]. As far as the researchers' knowledge is considered numerical solution of singularly perturbed boundary value problem containing both small delay and large delay is first being considered.…”

Existence of positive solutions for a class of semipositone problems with Kirchhoff operator

“…For example, considering the Laplacian operator, the authors in [23] show existence of radial solution in a ball or an annulus. For the case with the p-Laplacian operator, the authors in [29] found a positive solution in the critical case. A uniqueness result in exterior domains was proved in [14].…”