Abstract
In this article, we study the existence of solution for the following elliptic system of variable exponents with perturbation terms ∇div jrujp(x)∇2ru) + jujp(x)∇2u = γ a(x)juj(x)∇2u + Fu(x; u; v) in RN; ∇div jrvjq(x)∇2rv) + jvjq(x)∇2v = γ b(x)jvjγ (x)∇2v + Fv(x; u; v) in RN; u 2 W1;p(γ)(RN); v 2 W1;q(γ)(RN); where the corresponding functional does not satisfy PS conditions. We obtain a suγ cient condition for the existence of solution and also present a result on asymptotic behavior of solutions at inγ nity. where the corresponding functional does not satisfy PS conditions. We obtain a suffcient condition for the existence of solution and also present a result on asymptotic behavior of solutions at inffnity.
Original language | American English |
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Journal | Electronic Journal of Differential Equations |
Volume | 2015 |
State | Published - Mar 1 2015 |
Keywords
- Integral functional
- PS condition
- Variable exponent Sobolev space
- Variable exponent system
DC Disciplines
- Education
- Mathematics