Topological arguments for an elliptic equation involving the fractional Laplacian

The Solvability of Concave-Convex Quasilinear Elliptic Systems Involving $p$-Laplacian and Critical Sobolev Exponent

In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.

Existence of positive solutions to elliptic problems involving the fractional Laplacian

EXISTENCE THEOREMS FOR ELLIPTIC HEMIVARIATIONAL INEQUALITIES INVOLVING THE p-LAPLACIAN

Here, 2 ≤ p < ∞, j : Z × R → R is a function which is measurable in z ∈ Z and locally Lipschitz in x ∈ R and ∂ j(z,x) is the Clarke subdifferential of j(z, ·). If f : Z × R → R is a measurable function which is in general discontinuous in the x ∈ R variable, for almost all z ∈ Z, all M > 0, and all |x| ≤ M, we have | f (z,x)| ≤ aM(z) with aM ∈ L1(Z) and we set j(z,x) = ∫x 0 f (z, r)dr, then j(z...

An exponential spline for solving the fractional riccati differential equation

In this Article, proposes an approximation for the solution of the Riccati equation based on the use of exponential spline functions. Then the exponential spline equations are obtained and the differential equation of the fractional Riccati is discretized. The effect of performing this mathematical operation is obtained from an algebraic system of equations. To illustrate the benefits of the me...

Numerically solving an equation for fractional powers of elliptic operators

A boundary value problem for a fractional power of the second-order elliptic operator is considered. It is solved numerically using a time-dependent problem for a pseudo-parabolic equation. For the auxiliary Cauchy problem, the standard two-level schemes with weights are applied. Stability conditions are obtained for the fully discrete schemes under the consideration. The numerical results are ...