Pablo Alvarez-Caudevilla, Cristina Brandle, Devashish Sonowal
Abstract:
We establish the existence of positive solutions for a system of coupled fourth-order partial
differential equations on a bounded domain \(\Omega \subset \mathbb{R}^n\),
$$\displaylines{
\Delta^2u_1 +\beta_1 \Delta u_1-\alpha_1 u_1=f_1({ x},u_1,u_2),\cr
\Delta^2 u_2+\beta_2\Delta u_2-\alpha_2 u_2=f_2({ x},u_1,u_2),
}$$
for \(x\in\Omega\), subject to homogeneous Navier boundary conditions,
where the functions \(f_1,f_2 : \Omega\times [0,\infty)\times [0,\infty) \to [0,\infty)\)
are continuous, and \(\alpha_1,\alpha_2,\beta_1\) and \(\beta_2\) are real parameters satisfying certain constraints related to the eigenvalues of the associated Laplace operator.
Submitted August 14, 2024. Published May 29, 2025.
Math Subject Classifications: 35J70, 35J47, 35K57.
Key Words: Coupled system; higher order operator.
DOI: 10.58997/ejde.2025.56
Show me the PDF file (351 KB), TEX file for this article.
 |
Pablo Álvarez-Caudevilla Universidad Carlos III de Madrid Avenida de la Universidad, 30, 28911 Leganés Madrid, Spain email: pacaudev@math.uc3m.es |
|---|---|
 |
Cristina Brändle Universidad Carlos III de Madrid Avenida de la Universidad, 30, 28911 Leganés Madrid, Spain email: cbrandle@math.uc3m.es |
 |
Devashish Sonowal Universidad Carlos III de Madrid Avenida de la Universidad, 30, 28911 Leganés Madrid, Spain email: devashish.sonowal@iit.comillas.edu |
Return to the EJDE web page