A recent multiplicity theorem for the critical points of a functional defined on a finite– dimensional Hilbert space, established by Ricceri, is extended. An application to Dirichlet boundary value problems for difference equations involving the discrete p–Laplacian operator is presented. Mathematics Subject Classification (2000): 39A10, 47J30.

In this paper, we study the existence of monotone positive solutions for the following nonlinear m-point singular boundary value problem with p-Laplacian operator. The main tool is the monotone iterative technique. We obtain not only the existence of positive solutions for the problem, but also establish iterative schemes for approximating solution.

We study oscillatory behavior of a class of fourth-order neutral differential equations with a p-Laplacian like operator using the Riccati transformation and integral averaging technique. A Kamenev-type oscillation criterion is presented assuming that the noncanonical case is satisfied. This new theorem complements and improves a number of results reported in the literature. An illustrative exa...

In this article, by combining a recent critical point theorem and several theories of the ψ-Caputo fractional operator, multiplicity results at least three distinct weak solutions are obtained for new ψ-Caputo-type differential system including generalized p-Laplacian operator. It is noted that nonlinear functions do not need to adapt certain asymptotic conditions in paper, but, instead, replac...

We investigate quantitative properties of nonnegative solutions u(x) ≥ 0 to the semilinear diffusion equation Lu = f(u), posed in a bounded domain Ω ⊂ R with appropriate homogeneous Dirichlet or outer boundary conditions. The operator L may belong to a quite general class of linear operators that include the standard Laplacian, the two most common definitions of the fractional Laplacian (−∆) (0...

In this paper, we investigate the existence of positive solutions for a system of nonlinear fractional differential equations nonlocal boundary value problems with parameters and p-Laplacian operator. Under different combinations of superlinearity and sublinearity of the nonlinearities, various existence results for positive solutions are derived in terms of different values of parameters via t...

In this paper, we present a new proof of the upper and lower bound estimates for the first Dirichlet eigenvalue λ1 (B (p, r)) of Laplacian operator for the manifold with Ricci curvature Rc ≥ −K, by using Li-Yau’s gradient estimate for the heat equation.