This article focuses on the nonplanar traveling fronts of degenerate monostable time periodic reaction-diffusion equations in Rn with n≥3. By constructing a couple proper supersolution and subsolution, we prove existence pyramidal front R3 then n>3.

In this paper, we consider the Monge-Amp\`{e}re type equations on compact almost Hermitian manifolds. We derive $C^{\infty}$ a priori estimates under existence of an admissible $\mathcal{C}$-subsolution. Finally, obtain result if there exists supersolution.

By revisiting an asymptotic integration theory of nonlinear ordinary differential equations due to J.K. Hale and N. Onuchic [Contributions Differential Equations 2 (1963), 61–75], we improve and generalize several recent results in the literature. As an application, we study the existence of bounded positive solutions to a large class of semi-linear elliptic partial differential equations via t...

We study positive supersolutions to an elliptic equation (∗) −∆u = c|x|u, p, s ∈ R, in cone–like domains in R (N ≥ 2). We prove that in the sublinear case p < 1 there exists a critical exponent p∗ < 1 such that equation (∗) has a positive supersolution if and only if −∞ < p < p∗. The value of p∗ is determined explicitly by s and the geometry of the cone.

* Correspondence: [email protected] Department of Mathematics, Jiangxi Vocational College of Finance and Economics, Jiujiang, Jiangxi, 332000, PR China Abstract This paper deals with the critical parameter equations for a degenerate parabolic system coupled via nonlinear boundary flux. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence pa...

In this paper, we consider the deformed Hermitian-Yang-Mills equation on closed almost Hermitian manifolds. case of hypercritical phase, derive a priori estimates under existence an admissible \({\cal C}\)-subsolution. As application, prove solutions for condition supersolution.

This paper is concerned with time periodic V-shaped traveling fronts in reaction-diffusion equations ignition time-periodic nonlinearity. Our study mainly includes two parts: the first part we establish existence of by constructing a pair proper supersolution and subsolution, second prove uniqueness global asymptotic stability fronts.