Nontrivial solutions of a semilinear elliptic problem with resonance at zero
نویسندگان
چکیده
منابع مشابه
Nontrivial solutions of elliptic semilinear equations at resonance
We find nontrivial solutions for semilinear boundary value problems having resonance both at zero and at infinity.
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where Ω ⊂ R (N ≥ 1) is a bounded smooth domain, λk is an eigenvalue of the problem −Δu = λu in Ω, u = 0 on ∂Ω, and f : Ω × R → R is a Carathéodory function. If f(x, 0) = 0 for a.e. x ∈ Ω the constant u = 0 is a trivial solution of the problem (P). In this case, the key point is proving the existence of nontrivial solutions for (P). For this purpose, we need to introduce some conditions on the b...
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In recent years several nonlinear techniques have been very successful in proving the existence of weak solutions for semilinear elliptic boundary value problems at resonance. One technique involves a variational approach where solutions are characterized as saddle points for a related functional. This argument requires that the Palais-Smale condition and some coercivity conditions are satisfie...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2014
ISSN: 0893-9659
DOI: 10.1016/j.aml.2014.03.020