2021
DOI: 10.48550/arxiv.2109.03274
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Multiplicity results for nonhomogeneous elliptic equations with singular nonlinearities

Abstract: This paper is concerned with the study of multiple positive solutions to the following elliptic problem involving a nonhomogeneous operator with nonstandard growth of p-q type and singular nonlinearitieswhere Ω is a bounded domain inLp,qu := div(|∇u| p−2 ∇u + |∇u| q−2 ∇u), 1 < p < q < ∞, γ ∈ (0, 1), and f is a continuous nondecreasing map satisfying suitable conditions. By constructing two distinctive pairs of strict sub and super solution, and using fixed point theorems by Amann [1], we prove existence of thr… Show more

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Cited by 2 publications
(3 citation statements)
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“…A strong comparison principle for p-q Laplace operator is proved in Proposition 7 of [11] which provides the Proposition 3.3 of our paper and that in turn can be used to prove a three solution theorem. Arora [3] has proved a result in this direction for the double phase operator. Though Remark 3.8 is an easy consequence of [3], we shall nevertheless conclude our paper showing the result for p Laplacian.…”
Section: Proposition 35 the Mapmentioning
confidence: 90%
See 1 more Smart Citation
“…A strong comparison principle for p-q Laplace operator is proved in Proposition 7 of [11] which provides the Proposition 3.3 of our paper and that in turn can be used to prove a three solution theorem. Arora [3] has proved a result in this direction for the double phase operator. Though Remark 3.8 is an easy consequence of [3], we shall nevertheless conclude our paper showing the result for p Laplacian.…”
Section: Proposition 35 the Mapmentioning
confidence: 90%
“…Arora [3] has proved a result in this direction for the double phase operator. Though Remark 3.8 is an easy consequence of [3], we shall nevertheless conclude our paper showing the result for p Laplacian. u δ ; u| ∂Ω = 0 for certain range of λ > 0 where p > 1, δ ∈ (0, 1) and Ω an arbitrary bounded domain in R N .…”
Section: Proposition 35 the Mapmentioning
confidence: 90%
“…Moreover, using the integral representation via Green function and maximum principle, they proved the sharp boundary behavior of the weak solution. For further issues on nonlocal and nonlinear singular problems, the interested reader can consult to the bibliographic references in [8,6,21,23,35].…”
Section: Previous Workmentioning
confidence: 99%