Uniqueness of positive radial solutions for a class of infinite semipositone \(p\)-Laplacian problems in a ball. (English) Zbl 1442.34041
The authors consider a mixed boundary value problem with \(p\)-Laplacian:
\[
-(r^{N-1}\phi(u'))' = \lambda r^{N-1}f(u) \quad \text{on } \ (0,1), \\
u'(0) = 0, \quad u(1) = 0,
\]
where \(\phi(z) = |z|^{p-2}z\), \(p > 1\), \(\lambda \in {\mathbb R}\), \(f:{\mathbb R}\to{\mathbb R}\) continuously differentiable on \((0,\infty)\). Sufficient conditions are given for the existence of unique positive solution for sufficiently large values of the parameter \(\lambda\).
These results are obtained by using previous results of the second author [J. Math. Anal. Appl. 383, No. 2, 619–626 (2011; Zbl 1223.35137)].
These results are obtained by using previous results of the second author [J. Math. Anal. Appl. 383, No. 2, 619–626 (2011; Zbl 1223.35137)].
Reviewer: Jan Tomeček (Olomouc)
MSC:
| 34B09 | Boundary eigenvalue problems for ordinary differential equations |
| 34B16 | Singular nonlinear boundary value problems for ordinary differential equations |
| 34B18 | Positive solutions to nonlinear boundary value problems for ordinary differential equations |
| 35J62 | Quasilinear elliptic equations |
Citations:
Zbl 1223.35137References:
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