‎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 ...

We consider a second-order nonlinear degenerate anisotropic parabolic equation in the case when flux vector is only continuous and nonnegative diffusion matrix bounded measurable. The concepts of entropy sub- supersolution Cauchy problem are introduced, so that solution this problem, understood sense Chen-Perthame, both an supersolution. It established maximum subsolutions also subsolution prob...

In this article, using the sub-supersolution method and Rabinowitztype global bifurcation theory, we prove some results on existence, uniqueness and multiplicity of positive solutions for some singular nonlocal elliptic problems.

Let E be a complete, separable metric space and A be an operator on Cb(E). We give an abstract definition of viscosity sub/supersolution of the resolvent equation λu − Au = h and show that, if the comparison principle holds, then the martingale problem for A has a unique solution. Our proofs work also under two alternative definitions of viscosity sub/supersolution which might be useful, in par...

In this paper we investigate numerically positive solutions of the equation −Δu = λu+u with Dirichlet boundary condition in a boundary domain Ω for λ > 0 and 0 < q < 1 < p < 2∗, we will compute and visualize the range of λ, this problem achieves a numerical solution. Keywords—positive solutions; concave-convex; sub-supersolution method; pseudo arclength method.

We establish the existence of multiple solutions for a nonvariational elliptic systems involving p(x)-Laplacian operator. The approach combines methods sub–supersolution and Leray–Schauder topological degree.

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 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.