The biharmonic heat operator on edge manifolds and non-linear fourth order equations

on the effect of linear & non-linear texts on students comprehension and recalling

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New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

On the Solvability of a Fourth Order Operator Differential Equations

We establish sufficient conditions for the solvability of a fourth order operator differential equation. These conditions are expressed in terms of operator coefficients. 1. Preliminaries In this paper we consider the problem P (d/dt)u = du dt4 +Au+ 4 ∑ j=0 Aj d4−ju dt4−j = f, (1.1) e1 ui(0) = 0, i = 0, 1, si ∈ {0, 1, 2, 3}, (1.2) e2 where f ∈ L2(R+,H), and A0, A1, A2, A3, A4 and A are unbounde...

Lower order eigenvalues of the biharmonic operator

Abstract In this paper we consider the lower order eigenvalues of biharmonic operator on compact Riemannian manifolds with boundary (possibly empty) and prove a type of general inequalities for them. In particular, we study the lower order eigenvalues of biharmonic operator on compact submanifolds of Euclidean spaces, of spheres, and of projective spaces. We obtain some estimates for lower orde...

Operator-valued tensors on manifolds

‎In this paper we try to extend geometric concepts in the context of operator valued tensors‎. ‎To this end‎, ‎we aim to replace the field of scalars $ mathbb{R} $ by self-adjoint elements of a commutative $ C^star $-algebra‎, ‎and reach an appropriate generalization of geometrical concepts on manifolds‎. ‎First‎, ‎we put forward the concept of operator-valued tensors and extend semi-Riemannian...