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Nodal solutions for fractional elliptic equations involving exponential critical growth
Author(s) -
Souza Manassés,
Batista Severo Uberlandio,
Luiz do Rêgo Thiago
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6145
Subject(s) - mathematics , lemma (botany) , nodal , dirichlet problem , mathematical analysis , nonlinear system , energy (signal processing) , mountain pass , constraint (computer aided design) , laplace operator , fractional laplacian , geometry , boundary value problem , medicine , ecology , statistics , physics , poaceae , quantum mechanics , biology , anatomy
In the present paper, we study the existence of least energy nodal solution for a Dirichlet problem driven by the1 2 − Laplacian operator of the following type:( − Δ )1 2u + V ( x ) u = f ( u )in ( a , b ) ,u = 0in R ∖ ( a , b ) ,where V : [ a , b ] → [ 0 , + ∞ ) is a continuous potential and f ( t ) is a nonlinearity that grows like exp ( t 2 ) as t → + ∞ . By using the constraint variational method and quantitative deformation lemma, we obtain a least energy nodal solution u for the given problem. Moreover, we show that the energy of u is strictly larger than twice the ground state energy.