2 results
On the existence of a nodal solution for p-Laplacian equations depending on the gradient
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View
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- 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.
On the Harnack inequality for quasilinear elliptic equations with a first-order term
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 148 / Issue 5 / October 2018
- Published online by Cambridge University Press:
- 22 February 2018, pp. 1075-1095
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- October 2018
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We consider weak solutions to
with p > 1, q ≥ max{p − 1, 1}. We exploit the Moser iteration technique to prove a Harnack comparison inequality for C1 weak solutions. As a consequence we deduce a strong comparison principle.
