We study the solutions with dead cores and the decay estimates for a parabolic p-Laplacian equation with absorption by suband supersolution method. Special attention is given to the case where the solution of the steady-state problem vanishes in an interior region.

In this paper it is shown that the sub-supersolution method works for age-dependent diffusive nonlinear systems with non-local initial conditions. As application, we prove the existence and uniqueness of positive solution for a kind of Lotka-Volterra systems, as well as the blow-up in finite time in a particular case.

In this paper, a priori estimates of positive solutions for sublinear elliptic equations are given in terms of thicknesses of domains. To this end, a supersolution is constructed by a composite function of a solution to an ordinary differential equation and a distance function. The results work efficiently in the case where the domain is an exterior or an interior of a convex set.

The existence of a negative solution, of a positive solution, and of a sign-changing solution to a Dirichlet eigenvalue problem with p-Laplacian and multi-valued nonlinearity is investigated via suband supersolution methods as well as variational techniques for nonsmooth functions. 2000 Mathematics subject classification: 35J20, 35J85, 49J40.

‎in this paper‎, ‎we study a class of boundary value problem‎ ‎involving the p-laplacian oprator and singular nonlinearities‎. ‎we‎ ‎analyze the existence a critical parameter $lambda^{ast}$ such‎ ‎that the problem has least one solution for‎ ‎$lambdain(0,lambda^{ast})$ and no solution for‎ ‎$lambda>lambda^{ast}.$ we find lower bounds of critical‎ ‎parameter $lambda^{ast}$‎. ‎we use the method ...

In this paper we show the existence and multiplicity of positive solutions using sub-supersolution method Mountain Pass Theorem in a general singular system which operator is not homogeneous neither linear.

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.

We show the existence of positive solutions for a class of singular elliptic systems with convection term. The approach combines sub and supersolution method with the pseudomonotone operator theory and perturbation arguments involving singular terms. 2000 Mathematics Subject Classi…cation: 35J50, 35J60, 35J75