Continuums of positive solutions for classes of non-autonomous and non-local problems with strong singular term

Carlos Alberto Santos; Lais Santos; Pawan Kumar Mishra

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arXiv · 1811.05051

Continuums of positive solutions for classes of non-autonomous and non-local problems with strong singular term

Carlos Alberto Santos·Lais Santos·Pawan Kumar Mishra

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Abstract

In this paper, we show existence of \textit{continuums} of positive solutions for non-local quasilinear problems with strongly-singular reaction term on a bounded domain in $\mathbb{R}^N$ with $N \geq 2$. We approached non-autonomous and non-local equations by applying the Bifurcation Theory to the corresponding $\epsilon$-perturbed problems and using a comparison principle for $W_{\mathrm{loc}}^{1,p}(\Omega)$-sub and supersolutions to obtain qualitative properties of the $\epsilon$-\textit{continuum} limit. Moreover, this technique empowers us to study a strongly-singular and non-homogeneous Kirchhoff problem to get the existence of a \textit{continuum} of positive solutions.

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Carlos Alberto Santos, Lais Santos, Pawan Kumar Mishra. 2018-11-13. Continuums of positive solutions for classes of non-autonomous and non-local problems with strong singular term. https://arxiv.org/abs/1811.05051

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