Semilinear Elliptic Equations for Beginners: Existence Results via the Variational Approach

By M. Badiale, E. Serra. 2010

219 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/aa6cc8dbc23b672242ba4044ca67a83f22ed914d

How researchers see this paper

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In Mathematical Physics

1. Boštjan Gabrovšek
2. Jijiang Sun
3. Lin Li
4. Matija Cencelj

In Numerical Analysis

1. Matija Cencelj

Citations in the corpus

• Infinitely many sign-changing solutions for Kirchhoff type problems in R3 (2019, background): “ts a sign-changing critical point uk such that I(uk) = ck i.e., (3.12) Kc k ∩ Q6= ∅. To prove (3.12), arguing by contradiction, we suppose Kc k ∩ Q= ∅.By Lemma 3.9, there exist ε>0 and a map η ∈ C([0,1] × E,E) such that η(1,·) is odd, η(1,u) = ufor u∈ Ick−2ε and (3.13) η(1,Ick+ε ∪ W) ⊂ Ick−ε ∪ W.”