Semilinear Elliptic Equation with Biharmonic Operator and Multiple Critical Nonlinearities-Reference-Cited by-同舟云学术

Semilinear Elliptic Equation with Biharmonic Operator and Multiple Critical Nonlinearities

Published:2015-11-01 Issue:4 Volume:15 Page:835-848
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Bhakta Mousomi¹

Affiliation:

1. Department of Science and Technology University of New England, Armidale, NSW-2350, Australia

Abstract

Abstract We study the existence and non-existence of nontrivial weak solution of

, where N ≥ 5,

and

. Using Pohozaev type of identity, we prove the non-existence result when 1 < q < 2**. On the other hand when the equation has multiple critical nonlinearities i.e. q = 2** and −(N − 2)2 ≤ μ < μ1, we establish the existence of nontrivial solution, using the Mountain-Pass theorem by Ambrosetti and Rabinowitz.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2015-0405/pdf

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