We give a new bound on the exponent for nonexistence of stable solutions to the biharmonic problem ∆u = u, u > 0 in R where p > 1, n ≥ 20.

In this paper, we extend the definition of p-harmonic and p-biharmonic maps between Riemannian manifolds. We present some new properties for generalized stable maps.

Abstract Our goal is to establish a hidden regularity result for solutions of time fractional Petrovsky systems. The order $$\alpha $$ α the Caputo derivative belongs interval (1, 2). We achieve such suitable class weak solutions.

Two-level additive Schwarz preconditioners are developed for the nonconforming P1 finite element approximation of scalar second-order symmetric positive definite elliptic boundary value problems, the Morley finite element approximation of the biharmonic equation, and the divergence-free nonconforming P1 finite element approximation of the stationary Stokes equations. The condition numbers of th...

We prove the decay in energy space for solution to defocusing biharmonic Hartree-Fock equations with mass-supercritical and energy-subcritical Choquard-type nonlinearity dimension d⩾3. treat both free perturbed by a potential case. As direct consequence, we obtain large-data scattering H2(Rd)N,N⩾1.

This paper makes a short study of Fredholm integral equations related to potential theory and elasticity, with a view to preparing the ground for their exploitation in the numerical solution of difficult boundary-value problems. Attention is drawn to the advantages of Fredholm's first equation and of Green's boundary formula. The latter plays a fundamental and hitherto unrecognized role in the ...