We consider a prototype of quasilinear elliptic variational-hemivariational inequalities involving the indicator function of some closed convex set and a locally Lipschitz functional. We provide a generalization of the fundamental notion of suband supersolutions on the basis of which we then develop the sub-supersolution method for variationalhemivariational inequalities. Furthermore, we give a...

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.

The paper develops a sub-supersolution approach for quasilinear elliptic equations driven by degenerated p-Laplacian and containing convection term. presence of the operator forces substantial change to functional setting previous works. existence location solutions through is established. abstract result applied find nontrivial, nonnegative bounded solutions.