Contents
Research Article
Soliton solutions for a class of Schrödinger equations with a positive quasilinear term and critical growth
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- 18 February 2022, pp. 279-301
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We consider the following class of quasilinear Schrödinger equations proposed in plasma physics and nonlinear optics $-\Delta u+V(x)u+\frac {\kappa }{2}[\Delta (u^{2})]u=h(u)$
in the whole two-dimensional Euclidean space. We establish the existence and qualitative properties of standing wave solutions for a broader class of nonlinear terms $h(s)$
with the critical exponential growth. We apply the dual approach to obtain solutions in the usual Sobolev space $H^{1}(\mathbb {R}^{2})$
when the parameter $\kappa >0$
is sufficiently small. Minimax techniques, Trudinger–Moser inequality and the Nash–Moser iteration method play an essential role in establishing our results.
Back Cover (IBC, OBC) and matter
PEM series 2 volume 65 issue 4 Cover and Back matter
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- 01 February 2023, pp. b1-b2
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PEM series 2 volume 65 issue 3 Cover and Back matter
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- 18 October 2022, pp. b1-b2
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PEM series 2 volume 65 issue 2 Cover and Back matter
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- 08 July 2022, pp. b1-b2
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Front Cover (OFC, IFC) and matter
PEM series 2 volume 65 issue 1 Cover and Front matter
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- 14 March 2022, pp. f1-f2
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Back Cover (IBC, OBC) and matter
PEM series 2 volume 65 issue 1 Cover and Back matter
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- Published online by Cambridge University Press:
- 14 March 2022, pp. b1-b2
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