POSITIVE SOLUTIONS FOR A FOURTH-ORDER QUASILINEAR EQUATION WITH CRITICAL SOBOLEV EXPONENT

2010 ◽  
Vol 12 (01) ◽  
pp. 1-33 ◽  
Author(s):  
EDERSON MOREIRA DOS SANTOS
Keyword(s):  
Hamiltonian System ◽  
Positive Solutions ◽  
Fourth Order ◽  
Quasilinear Equation ◽  
Critical Sobolev Exponent ◽  
Critical Growth ◽  
Positive Parameter ◽  
Sobolev Exponent

We consider a fourth-order quasilinear equation depending on a positive parameter ∊ and with critical growth. Such equation is equivalent to a critical Hamiltonian system and the main goal of this work is to prove the existence of at least two positive solutions when the parameter ∊ is sufficiently small.

Construction of dipole type singular solutions for a biharmonic equation with critical Sobolev exponent

2002 ◽  
Vol 2 (4) ◽  
Author(s):  
Sarni Baraket
Keyword(s):  
Fourth Order ◽  
Weak Solutions ◽  
Biharmonic Equation ◽  
Critical Sobolev Exponent ◽  
Singular Solutions ◽  
Invariant Equation ◽  
Conformally Invariant ◽  
Sobolev Exponent

AbstractIn this paper, we construct positive weak solutions of a fourth order conformally invariant equation on S

scholarly journals On the location of the peaks of least-energy solutions to semilinear Dirichlet problems with critical growth

2002 ◽  
Vol 7 (10) ◽  
pp. 547-561 ◽  
Author(s):  
Marco A. S. Souto
Keyword(s):  
Bounded Domain ◽  
Critical Sobolev Exponent ◽  
Critical Growth ◽  
Dirichlet Problems ◽  
Growth Problem ◽  
Sobolev Exponent ◽  
Least Energy Solutions ◽  
Least Energy

We study the location of the peaks of solution for the critical growth problem−ε 2Δu+u=f(u)+u 2*−1,u>0inΩ,u=0on∂Ω, whereΩis a bounded domain;2*=2N/(N−2),N≥3, is the critical Sobolev exponent andfhas a behavior likeup,1<p<2*−1.

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