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Estimates on spectral interval of validity of anti-maximum principle. (arXiv:1807.06804v1 [math.AP])
来源于:arXiv
The anti-maximum principle for the homogeneous Dirichlet problem to
$-\Delta_p = \lambda |u|^{p-2}u + f(x)$ with positive $f \in L^\infty(\Omega)$
states the existence of a critical value $\lambda_f > \lambda_1$ such that any
solution of this problem with $\lambda \in (\lambda_1, \lambda_f)$ is strictly
negative. In this paper, we give a variational upper bound for $\lambda_f$ and
study its properties. As an important supplementary result, we investigate the
branch of ground state solutions of the considered boundary value problem on
$(\lambda_1,\lambda_2)$. 查看全文>>