Multiplicity of positive solutions for a class of problems with critical growth in ℝN

Claudianor O. Alves; Daniel C. de Morais Filho; Marco A. S. Souto

doi:10.1017/S0013091507000028

Abstract

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Using variational methods, we establish the existence and multiplicity of positive solutions for the following class of problems:

where λ,β∈(0,∞), q∈(1,2*−1), 2*=2N/(N−2), N≥3, V,Z:ℝN→ℝ are continuous functions verifying some hypotheses.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

O. Alves, Claudianor H. Miyagaki, Olímpio and H. M. Soares, Sérgio 2012. Multi-bump solutions for a class of quasilinear equations on $R$. Communications on Pure & Applied Analysis, Vol. 11, Issue. 2, p. 829.

SHIRAI, Shin-ichi 2013. Nonlinear Schrödinger Equations with Steep Magnetic Well. Tokyo Journal of Mathematics, Vol. 36, Issue. 1,

Liang, Sihua and Zhang, Jihui 2015. Existence of Multi-bump Solutions for a Class of Quasilinear Schrödinger Equations in $${\mathbb{R}^{N}}$$ R N Involving Critical Growth. Milan Journal of Mathematics, Vol. 83, Issue. 1, p. 55.

Shirai, Shin-ichi 2015. Multi-bump solutions to a nonlinear Schrödinger equation with steep magnetic wells. Journal of Mathematical Physics, Vol. 56, Issue. 9, p. 091510.

Yang, Liu and Liu, Zhisu 2016. Multiplicity and concentration of solutions for fractional Schrödinger equation with sublinear perturbation and steep potential well. Computers & Mathematics with Applications, Vol. 72, Issue. 6, p. 1629.

Huang, Yisheng Liu, Zeng and Wu, Yuanze 2016. On a Biharmonic Equation with Steep Potential Well and Indefinite Potential. Advanced Nonlinear Studies, Vol. 16, Issue. 4, p. 699.

Alves, Claudianor O. and Nóbrega, Alânnio B. 2017. Existence of multi-bump solutions for a class of elliptic problems involving the biharmonic operator. Monatshefte für Mathematik, Vol. 183, Issue. 1, p. 35.

Tang, Zhongwei and Wang, Lushun 2017. Solutions for the Problems Involving Fractional Laplacian and Indefinite Potentials. Advanced Nonlinear Studies, Vol. 17, Issue. 3, p. 551.

Song, Yueqiang and Shi, Shaoyun 2017. Existence and multiplicity results for a class of quasilinear Schrödinger equations in involving critical growth. Complex Variables and Elliptic Equations, Vol. 62, Issue. 7, p. 967.

Liang, Sihua and Shi, Shaoyun 2017. On multi-bump solutions of nonlinear Schrödinger equation with electromagnetic fields and critical nonlinearity in $$\mathbb {R}^N$$ R N. Calculus of Variations and Partial Differential Equations, Vol. 56, Issue. 2,

Alves, Claudianor O. and Pereira, Denilson S. 2017. Multiplicity of Multi-Bump Type Nodal Solutions for A Class of Elliptic Problems with Exponential Critical Growth in ℝ2. Proceedings of the Edinburgh Mathematical Society, Vol. 60, Issue. 2, p. 273.

Li, Peiluan and Yuan, Yuan 2018. Energy solutions and concentration problem of fractional Schrödinger equation. Boundary Value Problems, Vol. 2018, Issue. 1,

Wang, Youjun and Li, Zhouxin 2018. Existence of Solutions to Quasilinear Schrödinger Equations Involving Critical Sobolev Exponent. Taiwanese Journal of Mathematics, Vol. 22, Issue. 2,

Alves, Claudianor O. and Barros, Luciano M. 2018. Existence and multiplicity of solutions for a class of elliptic problem with critical growth. Monatshefte für Mathematik, Vol. 187, Issue. 2, p. 195.

Marcos do Ó, João Souto, Marco and Ubilla, Pedro 2020. Stationary Kirchhoff equations involving critical growth and vanishing potential. ESAIM: Control, Optimisation and Calculus of Variations, Vol. 26, Issue. , p. 74.

Ji, Chao and Rădulescu, Vicenţiu D. 2021. Multi-bump solutions for quasilinear elliptic equations with variable exponents and critical growth in ℝN. Communications in Contemporary Mathematics, Vol. 23, Issue. 05, p. 2050013.

Ji, Chao 2021. Multi-bump type nodal solutions for a logarithmic Schrödinger equation with deepening potential well. Zeitschrift für angewandte Mathematik und Physik, Vol. 72, Issue. 2,

Ji, Chao and Rădulescu, Vicenţiu D. 2021. Multi-bump solutions for the nonlinear magnetic Schrödinger equation with exponential critical growth in $${\mathbb {R}}^{2}$$. manuscripta mathematica, Vol. 164, Issue. 3-4, p. 509.

Alves, Claudianor O. and Ji, Chao 2022. Multi-bump positive solutions for a logarithmic Schrödinger equation with deepening potential well. Science China Mathematics, Vol. 65, Issue. 8, p. 1577.

Ji, Chao and Rădulescu, Vicenţiu D. 2022. Multi-bump solutions for the nonlinear magnetic Choquard equation with deepening potential well. Journal of Differential Equations, Vol. 306, Issue. , p. 251.

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Article contents

Multiplicity of positive solutions for a class of problems with critical growth in ℝN

Abstract

Keywords

MSC classification

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

Multiplicity of positive solutions for a class of problems with critical growth in ℝN

Abstract

Keywords

MSC classification

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