Positive solutions for P-Laplace problems with nonlinear time-fractional differential equation

Positive solutions for P-Laplace problems with nonlinear time-fractional differential equation

In this paper, we study the existence and multiplicity of positive solutions for semi-linear elliptic equations with a sign-changing weight function in weighted Sobolev spaces. By investigating the compact embedding theorem and based on the extraction of the Palais-Smale sequence in the Nehari manifold which is a subset of the weighted Sobolev spaces, we derive the existence of the multiple pos...

Positive Solution for P-laplace Problems with Nonlinear Time-fractional Differential Equation

In recent years, fractional differential equations are widely used in the many academic disciplines--viscoelastic mechanics, Fractal theory and so on. Furthermore, fractional differential equations can be used to describe some abnormal phenomenon. For instance, fractional convection-diffusion equation can be used to describe the fluid of abnormal infiltration phenomenon in the medium. In this p...

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

Triple Positive Solutions for Boundary Value Problem of a Nonlinear Fractional Differential Equation

Existence of Positive Solutions for a Nonlinear Fractional Differential Equation

Using the Schauder fixed point theorem, we prove an existence of positive solutions for the fractional differential problem in the half line R+ = (0,∞): Du = f(x, u), lim x→0+ u(x) = 0, where α ∈ (1, 2] and f is a Borel measurable function in R+ × R+ satisfying some appropriate conditions.