Critical growth elliptic problems with Choquard type nonlinearity: a survey. (English) Zbl 1529.35290
Manchanda, Pammy (ed.) et al., Mathematical modelling, optimization, analytic and numerical solutions. Selected papers based on the presentations at the international conference in conjunction with 14th biennial conference of ISIAM, Guru Nanak Dev University, Amritsar, India, February 2–4, 2018. Singapore: Springer. Ind. Appl. Math., 197-229 (2020).
Summary: 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.
For the entire collection see [Zbl 1460.65004].
For the entire collection see [Zbl 1460.65004].
MSC:
| 35K86 | Unilateral problems for nonlinear parabolic equations and variational inequalities with nonlinear parabolic operators |
Keywords:
Hardy-Littlewood-Sobolev inequality; critical exponent problem; nonlocal elliptic equationsReferences:
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