Publication details
Elliptic Equations with Hardy Potential and Gradient-Dependent Nonlinearity
| Authors | |
|---|---|
| Year of publication | 2020 |
| Type | Article in Periodical |
| Magazine / Source | Advanced Nonlinear Studies |
| MU Faculty or unit | |
| Citation | |
| Web | https://doi.org/10.1515/ans-2020-2073 |
| Doi | http://dx.doi.org/10.1515/ans-2020-2073 |
| Keywords | Hardy Potential; Singular Solutions; Boundary Trace; Uniqueness; Critical Exponent; Gradient Term; Isolated Singularities |
| Description | Let Omega subset of R-N (N >= 3) be a C-2 bounded domain, and let delta be the distance to partial derivative Omega. We study equations (E-+/-), -L(mu)u +/- g(u, vertical bar del u vertical bar) = 0 in Omega, where L-mu = Delta + mu/delta(2), mu epsilon (0, 1/4] and g: R x R+ -> R+ is nondecreasing and locally Lipschitz in its two variables with g(0, 0) = 0. We prove that, under some subcritical growth assumption on g, equation (E+) with boundary condition u = v admits a solution for any nonnegative bounded measure on partial derivative Omega, while equation (E-) with boundary condition u = v admits a solution provided that the total mass of v is small. Then we analyze the model case g(s, t) = vertical bar s vertical bar(p) t(q) and obtain a uniqueness result, which is even new with mu = 0. We also describe isolated singularities of positive solutions to (E+) and establish a removability result in terms of Bessel capacities. Various existence results are obtained for (E-). Finally, we discuss existence, uniqueness and removability results for (E-+/-) in the case g(s, t) = vertical bar s vertical bar(p) + t(q). |
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