Existence of solutions for a biharmonic equation with gradient term
DOI:
https://doi.org/10.24193/subbmath.2023.4.14Keywords:
Radial solution, Biharmonic equation, index theory, existenceAbstract
In this paper, we mainly study the existence of radial solutions for a class of biharmonic equation with a convection term, involving two real parameters \(\lambda\) and \(\rho\). We mainly use a combination of the fixed point index theory and the Banach contraction theorem to prove that there are $\lambda_0>0$ and \(\rho_0>0\) such the equation admits at least one radial solution
for all \((\lambda, \rho)\in \left[-\lambda_0,\infty\right[ \times
[0,\rho_0].\)
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