Multiple positive solutions to elliptic boundary blow-up problems
| Autor: | Alberto Boscaggin, Walter Dambrosio, Duccio Papini |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Weight function
Applied Mathematics 010102 general mathematics Mathematical analysis Shooting method Zero (complex analysis) Ode Boundary (topology) Radial solutions Function (mathematics) Boundary blow-up Indefinite weight Analysis 01 natural sciences 010101 applied mathematics Mathematics - Analysis of PDEs FOS: Mathematics Homoclinic orbit 0101 mathematics Analysis of PDEs (math.AP) Mathematical physics Mathematics |
| Zdroj: | Journal of Differential Equations. 262:5990-6017 |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2017.02.025 |
| Popis: | We prove the existence of multiple positive radial solutions to the sign-indefinite elliptic boundary blow-up problem { Δ u + ( a + ( | x | ) − μ a − ( | x | ) ) g ( u ) = 0 , | x | 1 , u ( x ) → ∞ , | x | → 1 , where g is a function superlinear at zero and at infinity, a + and a − are the positive/negative part, respectively, of a sign-changing function a and μ > 0 is a large parameter. In particular, we show how the number of solutions is affected by the nodal behavior of the weight function a . The proof is based on a careful shooting-type argument for the equivalent singular ODE problem. As a further application of this technique, the existence of multiple positive radial homoclinic solutions to Δ u + ( a + ( | x | ) − μ a − ( | x | ) ) g ( u ) = 0 , x ∈ R N , is also considered. |
| Databáze: | OpenAIRE |
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