We study the existence and nonexistence of positive solution to the problem
where is a smooth bounded domain in . We show the existence of a value such that when , there is a solution and when there is no solution in . Moreover as , the minimal positive solution converges to a solution. We also prove that there exists with , and for , such that the above problem does not have solution even in the distributional sense/very weak sense, and there is a complete blow-up. Under an additional integrability condition on b, we establish the uniqueness of positive solution.
Submitted February 5, 2016. Published September 28, 2016.
Math Subject Classifications: 35B09, 35B25, 35B35, 35G30, 35J91.
Key Words: Semilinear biharmonic equation; singular potential; Navier boundary condition; existence; nonexistence; blow-up phenomenon; stability; uniqueness of extremal solution.
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| Mousomi Bhakta |
Department of Mathematics
Indian Institute of Science Education and Research
Dr. Homi Bhaba road
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