Publication details
On critical double phase Kirchhoff problems with singular nonlinearity
| Authors | |
|---|---|
| Year of publication | 2022 |
| Type | Article in Periodical |
| Magazine / Source | Rendiconti del Circolo Matematico di Palermo Series 2 |
| MU Faculty or unit | |
| Citation | |
| Web | https://link.springer.com/article/10.1007/s12215-022-00762-7 |
| Doi | http://dx.doi.org/10.1007/s12215-022-00762-7 |
| Keywords | Critical growth; Double phase operator; Fibering method; Nehari manifold; Nonlocal Kirchhof term; Singular problem |
| Description | The paper deals with the following double phase problem -m[integral(Omega) (vertical bar del u vertical bar(p)/p+a(x)vertical bar del u vertical bar(p)/q)dx]div(vertical bar del u vertical bar(p-2)del u+a(x)vertical bar del u vertical bar(q-2)del u) = lambda u(-gamma) + u(p*-1) in Omega, u > 0 in Omega, u = 0 on partial derivative Omega, where Omega subset of R-N is a bounded domain with Lipschitz boundary partial derivative Omega, N >= 2, m represents a Kirchhoff coefficient, 1 < p < q < p* with p* = Np/(N - p) being the critical Sobolev exponent to p, a bounded weight a(center dot) >= 0, lambda > 0 and gamma is an element of(0, 1). By the Nehari manifold approach, we establish the existence of at least one weak solution. |
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