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Master's Dissertation
DOI
10.11606/D.55.2010.tde-13052010-095550
Document
Author
Full name
Moreno Pereira Bonutti
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2010
Supervisor
Committee
Soares, Sérgio Henrique Monari (President)
Massa, Eugenio Tommaso
Souto, Marco Aurélio Soares
Title in Portuguese
Multiplicidade de soluções positivas de uma equação de Schrödinger não linear
Keywords in Portuguese
Soluções positivas Schrödinger
Abstract in Portuguese
Este trabalho é dedicado ao estudo da existência de soluções da equação de Schrödinger 'DELTA'u + ('lambda' a(x) + 1)u = ' u POT. p, u > 0 em 'R POT. N', onde a '> ou =' 0 é uma função contínua e p > 1 é um expoente subcrítico. Métodos Variacionais são empregados para mostrar a existência de uma sequência ' lambda' IND. n' ' SETA' + 'INFINITO' e da respectiva sequência de soluções 'u IND. lambda IND. n' convergindo para uma solução de energia mínima do problema de Dirichlet - 'DELTA' u + u = 'u POT. p', ; u > 0em 'OMEGA', u = 0 sobre 'partial'' OMEGA", sendo "OMEGA' := int 'a POT. -1' (0). Além disso, estuda-se o efeito da topologia do conjunto 'OMEGA' sobre o número de soluções da equação (*) por meio da categoria de Lusternik e Schnirelman
Title in English
Multiple positive solutions for a nonlinear Schrödinger equations
Keywords in English
Positive solutions Schrödinger
Abstract in English
This work is devoted to study the existence of positive solutions of the Schrödinger equation 'DELTA'u + ('lambda'a(x) + 1)u = ' u POT. p', u > 0 in 'R POT. N', where a is a nonnegative and continuous function and p > 1 is a subcritical exponent. Variational methods are employed in order to show the existence of a sequence 'lambda' IND. n' "ARROW' + 'THE INFINITE' and the respective sequence of solutions converging in 'H POT. 1' ('R POT.N' ) to a least energy solution of the Dirichlet problem - 'DELTA'u + u = 'u POT. p' ; u > 0 in 'OMEGA', u = 0 on 'partial' ' OMEGA', where 'OMEGA' : = int 'a POT. -1 (0) Furthermore, it is studied the effect of the topology of the set 'OMEGA' on the number of positive solutions of the equation (*) by using the Lusternik and Schnirelman category
 
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Publishing Date
2010-05-13
 
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