Positive solutions for n-dimensional fourth-order systems under a parametric condition
We establish the existence of positive solutions for a system of coupled fourth-order partial differential equations on a bounded domain $\Omega \subset \mathbb{R}^n$, $$\displaylines{ \Delta^2u_1 +\beta_1 \Delta u_1-\alpha_1 u_1=f_1({ x},u_1,u_2),\cr \Delta^2 u_2+\beta_2\Delta u_2-\alpha_2 u_2=f...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2025-05-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2025/56/abstr.html |
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| Summary: | We establish the existence of positive solutions for a system of coupled fourth-order partial
differential equations on a bounded domain $\Omega \subset \mathbb{R}^n$,
$$\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. |
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| ISSN: | 1072-6691 |