Results 81 to 90 of about 9,477 (197)

Nonlinear biharmonic equations with negative exponents

Journal of Differential Equations, 2009
The authors study positive solutions of the equation \[ \Delta^2 u + u^{-q} = 0 \quad\text{in}\quad {\mathbb R}^3, \leqno(1) \] where \(q>0\) is a constant. This equation arises in conformal geometry in the following way. Given a smooth Riemannian manifold \((M,g)\) with \(n=\text{dim}\, M \geq 3\), the Paneitz operator is defined by \[ P_g = \Delta_g ...
Choi, Y.S., Xu, X.
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On existence and multiplicity of solutions for a biharmonic problem with weights via Ricceri's theorem

Demonstratio Mathematica
In this work, we consider a special nondegenerate equation with two weights. We investigate multiplicity result of this biharmonic equation. Mainly, our purpose is to obtain this result using an alternative Ricceri’s theorem.
Unal Cihan
doaj   +1 more source

On the Existence and Behavior of Solution for p(x)-Biharmonic-Type Hyperbolic Equation With Nonlinear Damping and Variable Exponent Source

Journal of Mathematics
A fourth-order px-biharmonic-type hyperbolic equation with variable-exponent nonlinearities is considered. The global existence of solutions has been obtained by potential well theory and the continuous principle.
Billel Gheraibia, Safa M. Mirgani, Nouri Boumaza, Khaled Zennir   +3 more
doaj   +1 more source

Integral equations for biharmonic data completion

Inverse Problems & Imaging, 2019
A boundary integral based method for the stable reconstruction of missing boundary data is presented for the biharmonic equation. The solution (displacement) is known throughout the boundary of an annular domain whilst the normal derivative and bending moment are specified only on the outer boundary curve.
Roman Chapko, B. Tomas Johansson
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Continuum Limit of \(p\)-Biharmonic Equations on Graphs

SIAM Journal on Mathematical Analysis
This paper studies the $p$-biharmonic equation on graphs, which arises in point cloud processing and can be interpreted as a natural extension of the graph $p$-Laplacian from the perspective of hypergraph. The asymptotic behavior of the solution is investigated when the random geometric graph is considered and the number of data points goes to infinity.
Kehan Shi, Martin Burger
openaire   +3 more sources

Mixing cubic quasi-interpolation spline collocation method and optimal control techniques to solve polyharmonic (p=2 and p=3) problem

Results in Applied Mathematics
This paper solves the polyharmonic equation for the cases p = 2 and p = 3, using an optimal control approach combined with the cubic quasi-interpolation spline collocation method.
L. El Houari, A. Naji, F. Ghafrani, M. Lamnii   +3 more
doaj   +1 more source

The obstacle scattering for the biharmonic wave equation

Inverse Problems
Abstract In this paper, we consider the obstacle scattering problem for biharmonic wave equations with the Dirichlet boundary condition in both two and three dimensions. Firstly, some basic properties are derived for the scattered fields, which leads to a simple criterion for the uniqueness of the solution.
Chengyu Wu, Jiaqing Yang
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Existence of nontrivial solutions for biharmonic equations with critical growth

Electronic Journal of Differential Equations
We consider the biharmonic equation with critical Sobolev exponent, $$ \Delta^2u-\Delta u-\Delta(u^2)u+V(x)u=|u|^{2^{**}-2}u+\alpha |u|^{p-2}u,\quad \text{in }\mathbb{R}^N, $$ where $N> 4$, $\alpha>0$, $V(x)$ is a given potential, $2^{**}=\frac{2N}{N-4}$
Juhua He, Ke Wu, Fen Zhou
doaj  

On the Normal Stability of Triharmonic Hypersurfaces in Space Forms. [PDF]

J Geom Anal, 2023
Branding V.
europepmc   +1 more source

\(p\)-biharmonic parabolic equations with logarithmic nonlinearity

Electronic Journal of Differential Equations, 2019
Summary: We consider an initial-boundary-value problem for a class of p-biharmonic parabolic equation with logarithmic nonlinearity in a bounded domain.
Jiaojiao Wang, Changchun Liu
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