Abstract
In this paper, we are interested on the study of the nonexistence of nontrivial solutions for a class of partial differential equations, in unbounded domains. This leads us to extend these results to m-equations systems. The method used is based on energy type identities.
Highlights
The study of the nonexistence of nontrivial solutions of partial differential equations and systems is the subject of several works of many authors, by using various methods to obtain the necessary and sufficient conditions, so the studied problems admit only the null solutions
Where θ : Ω → R, is nonnegative, λ (t) > 0 of a class L∞ (R) , admit only the trivial solutions, u ≡ v ≡ 0
Summary
The study of the nonexistence of nontrivial solutions of partial differential equations and systems is the subject of several works of many authors, by using various methods to obtain the necessary and sufficient conditions, so the studied problems admit only the null solutions. R×∂ω, considered in H2(R × ω) ∩ L∞(R × ω), where ω = ]a1, b1[ × ]a2, b2[ and this equation does not admit nontrivial solutions if the following conditions holds f (0) = 0, 2F (u) − uf (u) ≤ 0. In this work similar results for a class of the partial differential equations and systems were obtained. 1 ≤ k ≤ m, where fk : Ω × Rm→ R,are real continuous functions, locally Lipschitz in ui, verifing fk(x, u1, ..., 0, ..., um) = 0, ∀ x ∈ Ω,.
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