MULTIPLICITY AND CONCENTRATION RESULTS FOR SOME NONLINEAR SCHROEDINGER EQUATIONS WITH THE FRACTIONAL p-LAPLACIAN

Ambrosio Vincenzo; Isernia Teresa

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MULTIPLICITY AND CONCENTRATION RESULTS FOR SOME NONLINEAR SCHROEDINGER EQUATIONS WITH THE FRACTIONAL p-LAPLACIAN

机译：分数阶p-Laplacian非线性薛定ED方程的多重性与集中结果。

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摘要

We consider a class of parametric Schrodinger equations driven by the fractional p-Laplacian operator and involving continuous positive potentials and nonlinearities with subcritical or critical growth. Using variational methods and Ljusternik-Schnirelmann theory, we study the existence, multiplicity and concentration of positive solutions for small values of the parameter.

机译：我们考虑一类由分数p-Laplacian算子驱动的参数Schrodinger方程，该方程涉及连续的正电势和具有亚临界或临界增长的非线性。使用变分方法和Ljusternik-Schnirelmann理论，我们研究了参数较小值时正解的存在性，多重性和集中性。

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来源
《Discrete and continuous dynamical systems》 |2018年第11期|5835-5881|共47页
作者
Ambrosio Vincenzo; Isernia Teresa;
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作者单位

EPFL SB CAMA Dept Math Stn 8 CH-1015 Lausanne Switzerland;

Univ Politecn Marche Dipartimento Ingn Ind & Sci Matemat Via Brecce Bianche 12 I-60131 Ancona Italy;

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正文语种 eng
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关键词
Fractional Schrodinger equation; fractional p-Laplacian operator; Nehari manifold; Ljusternik-Schnirelmann theory; critical growth;

机译：分数薛定inger方程;分数p-Laplacian算子;Nehari流形;Ljusternik-Schnirelmann理论;关键增长;

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1. Multiplicity and concentration of positive solutions for fractional p-Laplacian problem involving concave-convex nonlinearity [J] . Lou Qingjun, Luo Hua Nonlinear analysis. Real world applications . 2018,第期

机译：涉及凹凸非线性的分数P-LAPLACIAN问题的阳性解的多重和浓度
2. MULTIPLICITY AND CONCENTRATION OF SOLUTIONS FOR NONLINEAR FRACTIONAL ELLIPTIC EQUATIONS WITH STEEP POTENTIAL [J] . Peng Song, Xia Aliang Communications on pure and applied analysis . 2018,第3期

机译：具有陡峭潜力的非线性分数椭圆方程的多重和浓度
3. Multiplicity of Solutions for Fourth-Order Elliptic Equations with p-Laplacian and Mixed Nonlinearity [J] . Mediterranean journal of mathematics . 2020,第2期

机译：具有P-Laplacian和混合非线性的四阶椭圆方程的多种解决方案
4. FRACTIONAL GENERALIZATION OF GINZBURG-LANDAU AND NONLINEAR SCHROEDINGER EQUATIONS [C] . George M. Zaslavsky, Vasily E. Tarasov American Society of Mechanical Engineers(ASME)International Design Engineering Technical Conference and Computers and Information in Engineering Conference(DETC2005) vol.6 pt.6: International Conference on Multibody Systems, Nonlinear Dynamics, and Contr . 2005

机译：GINZBURG-LANDAU的分数阶广义和非线性Schroedinger方程
5. Applications of a nonlinear Ovsjannikov theorem to boundary control of nonlinear Schroedinger and Korteweg-de Vries equations. [D] . De Jager, Joel Perry. 1997

机译：非线性Ovsjannikov定理在非线性Schroedinger和Korteweg-de Vries方程的边界控制中的应用。
6. Multiplicity and asymptotic behavior of solutions to a class of Kirchhoff-type equations involving the fractional p-Laplacian [O] . Liejun Shen -1

机译：一类涉及分数p-Laplacian的Kirchhoff型方程解的多重性和渐近行为
7. Publisher’s Note: “Existence and multiplicity of solutions for the fractional p-Laplacian Choquard logarithmic equation involving a nonlinearity with exponential critical and subcritical growth” J. Math. Phys. 62, 051507 (2021) [O] . Eduardo de S. Böer, Olímpio H. Miyagaki 2021

机译：发行商注意事项：“具有指数临界和亚临界生长的非线性的分数P-LAPLACIAN Coquartmic方程的存在和多重性”J。数学。物理。 62,051507（2021）
8. Symmetry analysis and Ansatzes for Schroedinger equations with the logarithmic nonlinearity [R] . Fushchych, W, Chopyk, V 1993

机译：具有对数非线性的schroedinger方程的对称性分析与ansatzes

MULTIPLICITY AND CONCENTRATION RESULTS FOR SOME NONLINEAR SCHROEDINGER EQUATIONS WITH THE FRACTIONAL p-LAPLACIAN

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