In this paper, by introducing a relativistic Schrödinger tempered fractional p-Laplacian operator (–Δ)p,λs,m, based on the (–Δ + m2)s and Laplacian (Δ λ)β/2, we consider model involving logarithmic nonlinearity. We first establish maximum principle boundary estimate, which play very crucial role in later process. Then obtain radial symmetry monotonicity results using direct method of moving pla...

We discuss the asymptotic behavior of positive solutions of the quasilinear elliptic problem −∆pu = au p−1 − b(x)u, u|∂Ω = 0 as q → p − 1 + 0 and as q → ∞ via a scale argument. Here ∆p is the p-Laplacian with 1 < p < ∞ and q > p−1. If p = 2, such problems arise in population dynamics. Our main results generalize the results for p = 2, but some technical difficulties arising from the nonlinear d...

Weak solutions and blow-up for wave equations of p-Laplacian type with supercritical sources" (2015). This paper investigates a quasilinear wave equation with Kelvin-Voigt damping, u t t − ∆ p u − ∆u t = f (u), in a bounded domain Ω ⊂ R 3 and subject to Dirichlét boundary conditions. The operator ∆ p , 2 < p < 3, denotes the classical p-Laplacian. The nonlinear term f (u) is a source feedback t...