The purpose of this paper is to study the Schwarz–Pick type inequality and Lipschitz continuity for solutions nonhomogeneous biharmonic equation: $$\Delta (\Delta f)=g$$ , where g : $$\overline{{\mathbb D}}\rightarrow {\mathbb {C}}$$ a continuous function D}}$$ denotes closure unit disk $${\mathbb D}$$ in complex plane . In fact, we establish following properties these solutions: First, show th...

Abstract Polyharmonic maps of order k (briefly, - harmonic ) are a natural generalization and biharmonic maps. These defined as the critical points suitable higher-order functionals which extend classical energy functional for between Riemannian manifolds. The main aim this paper is to investigate so-called unique continuation principle . More precisely, assuming that domain connected, we shall...

In an arbitrary bounded 2-D domain, a singular perturbation approach is developed to analyze the asymptotic behavior of several biharmonic linear and nonlinear eigenvalue problems for which the solution exhibits a concentration behavior either due to a hole in the domain, or as a result of a nonlinearity that is non-negligible only in some localized region in the domain. The specific form for t...

This article shows the existence and multiplicity of weak solutions for the (p, q)-biharmonic type system ∆(|∆u|p−2∆u) = λFu(x, u, v) in Ω, ∆(|∆v|q−2∆v) = λFv(x, u, v) in Ω, u = v = ∆u = ∆v = 0 on ∂Ω. Under certain conditions on F , we show the existence of infinitely many weak solutions. Our technical approach is based on Bonanno and Molica Bisci’s general critical point theorem.