Infinitely Many Solutions for Semilinear ∆γ-Differential Equations in RN without the Ambrosetti-Rabinowitz Condition
Keywords:
∆γ-Laplace problems, Cerami condition, variational method, weak solutions, Moun tain Pass Theorem.Abstract
We study the existence of infinitely many nontrivial solutions of the semilinear ∆γ-differential equations in RN −∆γu+b(x)u = f(x,u) in RN,
where ∆γ is the subelliptic operator of the type N ∆γ := j=1 ∂xj γ2 j∂xj , ∂xj := ∂ ∂xj , γ :=(γ1,γ2,...,γN), and the potential b(x) and nonlinearity f(x,u) are not assumed to be continuous, moreover f may not satisfy the Ambrosetti–Rabinowitz (AR) condition. Under some growth conditions on b and f, we show that there are infinitely many solutions to the problem.
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