QUASILINEAR EQUATIONS USING A LINKING STRUCTURE WITH CRITICAL NONLINEARITIES

doi:10.1007/s10473-022-0310-x

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (3): 975-1002.doi: 10.1007/s10473-022-0310-x

QUASILINEAR EQUATIONS USING A LINKING STRUCTURE WITH CRITICAL NONLINEARITIES

Edcarlos D. SILVA, Jefferson S. SILVA

Federal University of Goiás, Zip code 74001-970, Goiânia, Goiás-GO, Brazil

收稿日期:2020-09-09 修回日期:2020-10-14 发布日期:2022-06-24
通讯作者: Edcarlos D. SILVA,E-mail:edcarlos@ufg.br E-mail:edcarlos@ufg.br
基金资助:
Research was partially supported by CNPq with (429955/2018-9). The first author was partially suported by CNPq (309026/2020-2) and FAPDF with (16809.78.45403.25042017).

QUASILINEAR EQUATIONS USING A LINKING STRUCTURE WITH CRITICAL NONLINEARITIES

Edcarlos D. SILVA, Jefferson S. SILVA

Federal University of Goiás, Zip code 74001-970, Goiânia, Goiás-GO, Brazil

Received:2020-09-09 Revised:2020-10-14 Published:2022-06-24
Contact: Edcarlos D. SILVA,E-mail:edcarlos@ufg.br E-mail:edcarlos@ufg.br
Supported by:
Research was partially supported by CNPq with (429955/2018-9). The first author was partially suported by CNPq (309026/2020-2) and FAPDF with (16809.78.45403.25042017).

摘要/Abstract

摘要： It is to establish existence of a weak solution for quasilinear elliptic problems assuming that the nonlinear term is critical. The potential V is bounded from below and above by positive constants. Because we are considering a critical term which interacts with higher eigenvalues for the linear problem, we need to apply a linking theorem. Notice that the lack of compactness, which comes from critical problems and the fact that we are working in the whole space, are some obstacles for us to ensure existence of solutions for quasilinear elliptic problems. The main feature in this article is to restore some compact results which are essential in variational methods. Recall that compactness conditions such as the Palais-Smale condition for the associated energy functional is not available in our setting. This difficulty is overcame by taking into account some fine estimates on the critical level for an auxiliary energy functional.

关键词: Quasilinear Schrödinger equations, linking theorems, superlinear elliptic equations, critical nonlinearities, Bounded potentials

Abstract: It is to establish existence of a weak solution for quasilinear elliptic problems assuming that the nonlinear term is critical. The potential V is bounded from below and above by positive constants. Because we are considering a critical term which interacts with higher eigenvalues for the linear problem, we need to apply a linking theorem. Notice that the lack of compactness, which comes from critical problems and the fact that we are working in the whole space, are some obstacles for us to ensure existence of solutions for quasilinear elliptic problems. The main feature in this article is to restore some compact results which are essential in variational methods. Recall that compactness conditions such as the Palais-Smale condition for the associated energy functional is not available in our setting. This difficulty is overcame by taking into account some fine estimates on the critical level for an auxiliary energy functional.

Key words: Quasilinear Schrödinger equations, linking theorems, superlinear elliptic equations, critical nonlinearities, Bounded potentials

中图分类号:

35J20

Edcarlos D. SILVA, Jefferson S. SILVA. QUASILINEAR EQUATIONS USING A LINKING STRUCTURE WITH CRITICAL NONLINEARITIES[J]. 数学物理学报(英文版), 2022, 42(3): 975-1002.

Edcarlos D. SILVA, Jefferson S. SILVA. QUASILINEAR EQUATIONS USING A LINKING STRUCTURE WITH CRITICAL NONLINEARITIES[J]. Acta mathematica scientia,Series B, 2022, 42(3): 975-1002.

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QUASILINEAR EQUATIONS USING A LINKING STRUCTURE WITH CRITICAL NONLINEARITIES

QUASILINEAR EQUATIONS USING A LINKING STRUCTURE WITH CRITICAL NONLINEARITIES

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