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Singular Nonlocal Problem Involving Measure Data

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Abstract

In this paper we prove existence of solutions for a partial differential equation involving a singularity with a general nonnegative, Radon measure as source term which is given as

$$\begin{aligned} (-\Delta )^s u&= f(x)h(u)+\mu ~\text {in}~\Omega , \\ u&=0~\text {in}~\mathbb {R}^N{\setminus }\Omega , \\ u&> 0~\text {in}~\Omega , \end{aligned}$$

where \(\Omega \) is a bounded domain of \(\mathbb {R}^N\), f is a nonnegative function over \(\Omega \).

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Acknowledgements

Two of the authors, Sekhar Ghosh and Ratan Kr. Giri, thanks the financial assistantship received from the Council of Scientic and Industrial Research (CSIR), India and the Ministry of Human Resource Development (MHRD), Govt. of India respectively.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Rourkela, India

    Sekhar Ghosh, Debajyoti Choudhuri & Ratan Kr. Giri

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  1. Sekhar Ghosh
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  2. Debajyoti Choudhuri
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  3. Ratan Kr. Giri
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Correspondence to Debajyoti Choudhuri.

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Ghosh, S., Choudhuri, D. & Giri, R.K. Singular Nonlocal Problem Involving Measure Data. Bull Braz Math Soc, New Series 50, 187–209 (2019). https://doi.org/10.1007/s00574-018-0100-1

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  • DOI: https://doi.org/10.1007/s00574-018-0100-1

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