Existence Of Solutions For Classes Research Articles

Existance of solutions for some class of system quasilinear differentials with nonlocal boundary conditions and with nonlinearity depandant on the first derivate in time scales

This work is conserned with the construction of minimal and maximal solution for some equation quasilinear differentials with nonlocal boundary condition with nonlinearity is continuous function dependent on the first derivate in the time scale. In a previous study, see[11] it was found that there exists the extrimals solutions of a quasilinear elliptic system with intergral boundary conditions in the continuous case, and from here we asked the following question using the upper and lower solutions method coupled with monotone iterative technique and we asked the following question: do we have the existence of extrimals solutions for certain classes of systems of differential equations with nonlocal boundary conditions in time scales by same method. We can classify the problem following the monotonicity of the two functions and in the true types.Type 1: Increasing qasimonotonic systems.Type 2: Decreasing qasimonotonic systems. Type 3: Mexed qasimonotonic systems. In this paper we show the existence minimuls-maximuls solutions if the problem is of the type 1. If the problem is of the type 2 , we show the existence of maximuls-minimuls solutions. If the problem is of the type 3 , we show existence of least quasilear-solution. In the end, we gave examples of the results presented in this work to prove their validity through two cases: the continuous case, represented by the set of real numbers, and the discontinuous case, represented by the set of integers.

Coincidence point theorems in ordered Banach spaces and applications

In this paper, we study the existence of positive solutions for classes of nonlinear operator equations in Banach spaces ordered by cones. We establish new coincidence point theorems via a generalized monotone iterative method. As applications, we discuss the existence of positive solutions for systems of nonlinear matrix equations and a system of integral equations of Volterra type.

Quantitative local and global a priori estimates for fractional nonlinear diffusion equations

We establish quantitative estimates for solutions u(t,x) to the fractional nonlinear diffusion equation, ∂tu+(−Δ)s(um)=0 in the whole range of exponents m>0, 0<s<1. The equation is posed in the whole space x∈Rd. We first obtain weighted global integral estimates that allow to establish existence of solutions for classes of large data. In the core of the paper we obtain quantitative pointwise lower estimates of the positivity of the solutions, depending only on the norm of the initial data in a certain ball. The estimates take a different form in three exponent ranges: slow diffusion, good range of fast diffusion, and very fast diffusion. Finally, we show existence and uniqueness of initial traces.