Local “superlinearity” and “sublinearity” for the \(p\)-Laplacian. (English) Zbl 1178.35176
The authors obtain existence and multiplicity results for the parametric Dirichlet problem \(\Delta_p u+f_\lambda (x,u)=0\) set in a bounded domain, both in the subcritical and critical cases.
Also, as a by product, some improved strong comparison principles and \(C^{1,\alpha}\) estimates are given.
Also, as a by product, some improved strong comparison principles and \(C^{1,\alpha}\) estimates are given.
Reviewer: Enrico Valdinoci (Roma)
MSC:
| 35J62 | Quasilinear elliptic equations |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35B51 | Comparison principles in context of PDEs |
| 35B45 | A priori estimates in context of PDEs |
| 35B33 | Critical exponents in context of PDEs |
| 35J20 | Variational methods for second-order elliptic equations |
Keywords:
\(p\)-Laplacian; concave-convex nonlinearities; critical exponent; \(C_0^1\) versus \(W_0^{1,p}\) local minimization; strong comparison principle; \(C^{1, \alpha} \) estimate; upper-lower solutionsReferences:
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