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Critical Growth Elliptic Problems with Choquard Type Nonlinearity: A Survey

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Mathematical Modelling, Optimization, Analytic and Numerical Solutions

Part of the book series: Industrial and Applied Mathematics ((INAMA))

Abstract

This article deals with a survey of recent developments and results on Choquard equations where we focus on the existence and multiplicity of solutions of the partial differential equations which involves the nonlinearity of the convolution type. Because of its nature, these equations are categorized under the nonlocal problems. We give a brief survey on the work already done in this regard following which we illustrate the problems we have addressed. Seeking the help of variational methods and asymptotic estimates, we prove our main results.

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Authors and Affiliations

  1. Indian Institute of Technology Delhi, Hauz Khaz, New Delhi, 110016, India

    K. Sreenadh

  2. Tata Institute of Fundamental Research (TIFR) Centre of Applicable Mathematics, Bangalore, India

    T. Mukherjee

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  1. K. Sreenadh
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  2. T. Mukherjee
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Correspondence to K. Sreenadh .

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Editors and Affiliations

  1. Department of Mathematics, Guru Nanak Dev University, Amritsar, Punjab, India

    Pammy Manchanda

  2. Laboratory Math, J.A. Dieudonné, University Côte d’Azur, Nice, France

    René Pierre Lozi

  3. School of Basic Sciences and Research, Sharda University, Greater Noida, Uttar Pradesh, India

    Abul Hasan Siddiqi

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Sreenadh, K., Mukherjee, T. (2020). Critical Growth Elliptic Problems with Choquard Type Nonlinearity: A Survey. In: Manchanda, P., Lozi, R., Siddiqi, A. (eds) Mathematical Modelling, Optimization, Analytic and Numerical Solutions. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-15-0928-5_10

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