| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Estadual Campinas, Dept Math, BR-13083859 Campinas, SP - Brazil
[2] UNESP, Ibilce, Dept Math, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | QUARTERLY OF APPLIED MATHEMATICS; v. 76, n. 4, p. 699-711, DEC 2018. |
| Web of Science Citations: | 0 |
| Abstract | |
We consider the Laplace equation in the half-space satisfying a nonlinear Neumann condition with boundary potential. This class of problems appears in a number of mathematical and physics contexts and is linked to fractional dissipation problems. Here the boundary potential and nonlinearity are singular and of power-type, respectively. Depending on the degree of singularity of potentials, first we show a nonexistence result of positive solutions in D-1,D-2(R-+(n)) with a L-p-type integrability condition on partial derivative R-+(n). After, considering critical nonlinearities and conditions on the size and sign of potentials, we obtain the existence of positive solutions by means of minimization techniques and perturbation methods. (AU) | |
| FAPESP's process: | 12/10153-6 - Nonlinear Elliptic Equations with Singular Potentials |
| Grantee: | Sérgio Leandro Nascimento Neves |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |