Quasilinear elliptic equations with exponential nonlinearity and measure data

Abstract

Let normalΩ⊆double-struckRN be either a bounded domain or the entire space. This paper concerns existence and global pointwise estimates in terms of Wolff potentials of solutions to quasilinear and Hessian equations of Lane‐Emden type: −Δpu=σP(u)+ω,Fk[−u]=σP(u)+ω under minimal assumptions on σ and ω, where σ is an A∞ weight and ω is a nonnegative Borel measure, and Pfalse(ufalse)∼expγuβ with γ>0, β ≥ 1. Our methods are based on systematic application of Wolff potentials and good‐λ inequality for fractional maximal potential.

Existence of W01,1Ω Solutions to Non-Coercivity Quasiline

“…Under the hypothesis (11)- (14), the authors proved that (10) has at least a weak solution 푢 ∈ 푊 1,푝 0 (Ω) ∩ 퐿 ∞ (Ω) in the sense that for all v in 퐶 ∞ 0 (Ω). On the other hand, as in [22], it has been shown the existence results of solutions for nonlinear elliptic boundary value problem where 푓 ∈ 퐿 (푚 ⩾ 1), 1 < 푝 < 푁. We recall the following results contained in [22].…”

“…On the other hand, as in [22], it has been shown the existence results of solutions for nonlinear elliptic boundary value problem where 푓 ∈ 퐿 (푚 ⩾ 1), 1 < 푝 < 푁. We recall the following results contained in [22].…”

“…In order to prove the existence part of eorems 1 and 6 we need the following preliminary result. is convergence of the gradients is a consequence of a classical result (see [22]).…”

Spatiotemporal patterns induced by delay and cross‐fractional diffusion in a predator‐prey model describing intraguild predation

“…In the past decades, spatiotemporal dynamic patterns, especially in biology, mathematical ecology, and chemistry, have been investigated widely by many authors. [15][16][17][18][19][20][21][22][23][24][25][26][27] Currently, the spatiotemporal patterns of population distribution have been a hot topic because species abundance changes not only in time but also in space. Our first objective is to show that delay can induce spatially homogeneous and inhomogeneous periodic oscillatory patterns resulting from Hopf bifurcation.…”

Stability and Bifurcation for a Single-Species Model with Delay Weak Kernel and Constant Rate Harvesting

“…e study concerning population dynamics with harvesting is a subject of mathematical bioeconomics. e study on mathematical models of bioeconomics for resource management can be found in [4,[26][27][28][29][30][31][32][33][34]. Renewable resources, which are vital to human survival, are increasingly being overexploited.…”