Abstract
A system of quasilinear elliptic equations on an unbounded domain is considered. The existence of a sequence of radially symmetric weak solutions is proved via variational methods.
Highlights
We consider the following problem −∆pu + |u|p−2u =λα1(x)f1(v) in RN,−∆qv + |v|q−2v = λα2(x)f2(u) in RN, (1)u, v ∈ W 1,p(RN ), where p, q > N > 1
Partial differential equations are used to model a wide variety of physically significant problems arising in different areas such as physics, engineering and other applied disciplines
Sobolev spaces play an important role in the theory of partial differential equations as well as Orlicz-Morrey space and B ∞ −1,∞ space
Summary
By inspiration of [20], we prove the existence of a sequence of radially symmetric weak solutions for (1) in the unbounded domain RN . The following theorem is important to study the critical point of the functional. By standard arguments [5], we can show that Φ is Gateaux differentiable, coercive and sequentially weakly lower semicontinuous whose derivative at the point (u, v) ∈ X is the functional Φ (u, v) ∈ X∗ given by
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