Uniqueness of solutions of parabolic semilinear nonlocal-boundary problems

Uniqueness of Solutions for Fourth-order Nonlocal Boundary Value Problems

Uniqueness implies uniqueness relationships are examined among solutions of the fourth-order ordinary differential equation, y (4) = f (x, y, y , y , y), satisfying 5-point, 4-point, and 3-point nonlocal boundary conditions. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution , and reproduction in any medium, pr...

Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations

We investigate quantitative properties of nonnegative solutions u(x) ≥ 0 to the semilinear diffusion equation Lu = f(u), posed in a bounded domain Ω ⊂ R with appropriate homogeneous Dirichlet or outer boundary conditions. The operator L may belong to a quite general class of linear operators that include the standard Laplacian, the two most common definitions of the fractional Laplacian (−∆) (0...

Semilinear parabolic problems

Existence and uniqueness of solutions for p-laplacian fractional order boundary value problems

In this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-Laplacian fractional order differential equations. We use Schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. We include some examples to show the applicability of our results.

Propagation of Singularities of Solutions to Semilinear Boundary Value Problems

Let P be a second-order, strictly hyperbolic differential operator on an open region Q C R n (n > 3) with smooth noncharacteristic boundary. Given a solution u G fffoc(n), s > (n + l ) /2 , to Pu = f(x,u), we discuss the propagation of microlocal H singularities in the range s < r < 2s — n/2 in the general case where the Hamilton field of p may be tangent to dT* f2\0 to arbitrarily high finite ...