Journal•ISSN: 1536-1365
Advanced Nonlinear Studies
De Gruyter
About: Advanced Nonlinear Studies is an academic journal published by De Gruyter. The journal publishes majorly in the area(s): Nonlinear system & Sobolev space. It has an ISSN identifier of 1536-1365. Over the lifetime, 889 publications have been published receiving 11164 citations.
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TL;DR: In this paper, the authors obtained some non-existence results for the Klein{Gordon equation coupled with the electrostatic fleld, which relies on the deduction of some suitable Poho-zaev identity which provides necessary conditions to get existence.
Abstract: In this paper we obtain some non-existence results for the Klein{Gordon equation coupled with the electrostatic fleld. The method relies on the deduction of some suitable Poho‚zaev identity which provides necessary conditions to get existence ‡ ·
312 citations
TL;DR: In this paper, the standard Ambrosetti-Rabinowitz superlinear condition can be replaced by a more natural super-quadratic condition with a Nehari type condition.
Abstract: Abstract We present various results on multiple solutions for superlinear elliptic equations in a bounded domain or in the whole space. With a Nehari type condition assumed, we show that the standard Ambrosetti-Rabinowitz superlinear condition can be replaced by a more natural super-quadratic condition.
169 citations
TL;DR: In this paper, the concentration and multiplicity of weak solutions to the Kirch-hoff type equation with critical Sobolev growth was studied, and the authors showed that weak solutions can be found in a large number of locations.
Abstract: We study the concentration and multiplicity of weak solutions to the Kirch- hoff type equation with critical Sobolev growth
154 citations
TL;DR: In this article, the existence of standing wave solutions of nonlinear Schrödinger equation coupled with Maxwell equations which are non-radially symmetric is proved, which is the case for all the solutions of the standing wave solution.
Abstract: Abstract In this paper we prove the existence of standing wave solutions of nonlinear Schrödinger equation coupled with Maxwell equations which are non-radially symmetric.
141 citations
TL;DR: In this article, the existence and multiplicity of ground states and bound states in the Schrodinger system with large couplings is investigated. But the authors do not consider the case where the couplings are arbitrary.
Abstract: This paper concerns existence and multiplicity of ground states and bound states of the time-independent Schrodinger system 8 > > where n = 2;3, N ‚ 2, ‚j > 0 for j = 1;¢¢¢ ;N, fljj > 0 for j = 1;¢¢¢ ;N, and flij = flji. In the attractive case we give su-cient condition for existence of co-existing ground states with large couplings, and in the repulsive case we prove existence of inflnitely many co-existing bound state solutions with arbitrary couplings.
137 citations