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On the existence of a nodal solution for p-Laplacian equations depending on the gradient
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View
- Published online by Cambridge University Press:
- 31 January 2024, pp. 1-22
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In the present paper we deal with a quasi-linear elliptic equation depending on a sublinear nonlinearity involving the gradient. We prove 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. The same conclusion is obtained for an eigenvalue problem under a different set of assumptions.
