We deal with the existence and localization of positive radial solutions for Dirichlet problems involving ϕ $$ \phi -Laplacian operators in a ball. In particular, p Minkowski-curvature equations are considered. Our approach relies on fixed point index techniques, which work thanks to Harnack-type inequality terms seminorm. As consequence result, it is also derived several (even infinitely many)...

In this paper, we first establish a new fixed point theorem for a Meir-Keeler type condition. As an application, we derive a simultaneous generalization of Banach contraction principle, Kannan's fixed point theorem, Chatterjea's fixed point theorem and other fixed point theorems. Some new fixed point theorems are also obtained.

Abstract A newly proposed p -Laplacian nonperiodic boundary value problem is studied in this research paper the form of generalized Caputo fractional derivatives. The existence and uniqueness solutions are fully investigated for using some fixed point theorems such as Banach Schauder. This work supported with an example to apply all obtained new results validate their applicability.

We consider the multi-point discrete boundary value problem with one-dimensional p-Laplacian operator Δ φp Δu t − 1 q t f t, u t ,Δu t 0, t ∈ {1, . . . , n − 1} subject to the boundary conditions: u 0 0, u n ∑m−2 i 1 aiu ξi , where φp s |s|p−2s, p > 1, ξi ∈ {2, . . . , n − 2} with 1 < ξ1 < · · · < ξm−2 < n − 1 and ai ∈ 0, 1 , 0 < ∑m−2 i 1 ai < 1. Using a new fixed point theorem due to Avery and...

In a bounded open region of the d dimensional space we consider a Brownian motion which is reborn at a fixed interior point as soon as it reaches the boundary. The evolution is invariant with respect to a density equal, modulo a constant, to the Green function of the Dirichlet Laplacian centered at the point of return. We calculate the resolvent in closed form, study its spectral properties and...

In this article, we study the four-point boundary-value problem with the one-dimensional p-Laplacian (φpi (u ′ i)) ′ + qi(t)fi(t, u1, u2) = 0, t ∈ (0, 1), i = 1, 2; ui(0)− gi(ui(ξ)) = 0, ui(1) + gi(ui(η)) = 0, i = 1, 2. We obtain sufficient conditions such that by means of a fixed point theorem on a cone, there exist multiple symmetric positive solutions to the above boundary-value problem. As ...