| Abstract: |
| In this talk we deal with a quasi-linear elliptic equation depending on a
sublinear nonlinearity involving the gradient. Our aim is to combine variational techniques with fixed point theory in order to prove the existence of a positive solution.We prove also the existence of a nontrivial
nodal solution employing the theory of invariant sets of descending flow together
with sub-supersolution techniques, gradient regularity arguments, strong comparison
principle for the p-Laplace operator.
Based on the papers F. Faraci, D.Motreanu, D. Puglisi, Quasi-linear elliptic equations with dependence on the gradient, Calc. Var. Partial Differential Equations (2015) and F. Faraci, D. Puglisi, Nodal solutions of p-Laplacian equations depending on the gradient, Proc. Roy. Soc. Edinburgh A (2024). |
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