# On biharmonic maps and their generalizations

## Related Articles

- Regularity and relaxed problems of minimizing biharmonic maps into spheres. Hong, Min-Chun; Wang, Changyou // Calculus of Variations & Partial Differential Equations;Aug2005, Vol. 23 Issue 4, p425
For $n\ge 5$ and $k\ge 4$, we show that any minimizing biharmonic map from $\Omega\subset \Bbb R^n$ to S k is smooth off a closed set whose Hausdorff dimension is at most n-5. When n = 5 and k = 4, for a parameter $\lambda\in [0,1]$ we introduce a $\lambda$-relaxed energy $\Bbb H_{\lambda}$ of...

- A BIHARMONIC EQUATION IN INVOLVING â„4 NONLINEARITIES WITH CRITICAL EXPONENTIAL GROWTH. SANI, FEDERICA // Communications on Pure & Applied Analysis;Jan2013, Vol. 12 Issue 1, p405
In this paper we give sufficient conditions for the existence of solutions of a biharmonic equation of the form Î”uÂ² + V(x)u = f(u) in â„4 where V is a continuous positive potential bounded away from zero and the nonlinearity f(s) behaves like eÎ±Â°sÂ² at infinity for some Î±0...

- Multiple Solutions for Biharmonic Equations with Asymptotically Linear Nonlinearities. Ruichang Pei // Boundary Value Problems;2010, Special section p1
The existence of multiple solutions for a class of fourth elliptic equation with respect to the resonance and nonresonance conditions is established by using the minimax method and Morse theory.

- On the p-biharmonic equation involving concave-convex nonlinearities and sign-changing weight function. Chao Ji; Weihua Wang // Electronic Journal of Qualitative Theory of Differential Equatio;2012, Issue 1-24, p1
In this paper, we study the combined effect of concave and convex nonlinearities on the number of nontrivial solutions for the p-biharmonic equation of the form {Î”pÂ²u = |u|q-2u + Î»f(x)|u|r-2u in Î©, u = âˆ‡u = 0 on âˆ‚, (0.1) where Î© is a bounded domain in RN, f âˆˆ...

- Soliton ratchets in homogeneous nonlinear Klein-Gordon systems. Morales-Molina, Luis; Quintero, Niurka R.; Sánchez, Angel; Mertens, Franz G. // Chaos;Mar2006, Vol. 16 Issue 1, p013117
We study in detail the ratchetlike dynamics of topological solitons in homogeneous nonlinear Klein-Gordon systems driven by a biharmonic force. By using a collective coordinate approach with two degrees of freedom, namely the center of the soliton, X(t), and its width, l(t), we show, first, that...

- Nonlinear biharmonic boundary value problem. Tacksun Jung; Q-Heung Choi // Boundary Value Problems;Feb2014, Vol. 2014, p1
We consider the nonlinear biharmonic equation with variable coefficient and polynomial growth nonlinearity and Dirichlet boundary condition. We get two theorems. One theorem says that there exists at least one bounded solution under some condition. The other one says that there exist at least...

- The behavior of solutions of the nonlinear biharmonic equation in an unbounded domain. Neklyudov, A. // Mathematical Notes;Jan2014, Vol. 95 Issue 1/2, p224
Periodic (in one variable) solutions in the half-plane of the two-dimensional nonlinear biharmonic equation with exponential nonlinearity on the right-hand side are considered. The power-law and logarithmic asymptotics of the solutions at infinity are obtained.

- Expansion of the Distance between Two Points in Spheroidal Functions as Applied to Problems of Mathematical Physics. Baranov, A. S. // Technical Physics;Feb2002, Vol. 47 Issue 2, p177
A complete set of biharmonic functions is constructed in spheroidal coordinates. The distance between two points and its inverse value are expanded into a double series in terms of such functions. Possible applications in the theory of elasticity, in astrophysics, and other fields of...

- The Jeffery paradox as the limit of a three-dimensional Stokes flow. Smith, S. H. // Physics of Fluids A;May90, Vol. 2 Issue 5, p661
The solution of the biharmonic equation for the slow viscous flow resulting from a line rotlet in front of a circular cylinder indicates the physically unrealistic behavior of a uniform stream at infinityâ€”an example of the Jeffery paradox. It is shown here, when the three-dimensional...