| Title: | Jumping Unbounded Nonlinearities and ALP Condition |
| Authors: | Tomiczek, Petr |
| Citation: | TOMICZEK, P. Jumping Unbounded Nonlinearities and ALP Condition. WSEAS Transactions on Mathematics, 2022, roč. 21, č. April 2022, s. 196-206. ISSN: 1109-2769 |
| Issue Date: | 2022 |
| Publisher: | World Scientific and Engineering Academy and Society |
| Document type: | článek article |
| URI: | 2-s2.0-85133679468 http://hdl.handle.net/11025/50948 |
| ISSN: | 1109-2769 |
| Keywords in different language: | Second order ODE;periodic;resonance;jumping nonlinearities;Dancer-Fucik spectrum;ALPcondition;saddle point theorem |
| Abstract in different language: | We investigate the existence of solutions to the nonlinear problem u′′(x) + λ_+u^+(x) − λ_−u^−(x) + g(x, u(x)) = f (x) , x ∈ (0, 2π) , u(0) = u(2π) , u′(0) = u′(2π) ,where the point [λ_+, λ_−] is a point of the Fučík spectrum Σ = ⋃ Σ_m. We denote φ_m any nontrivial solution toour problem with g = f = 0 corresponding to [λ_+, λ_−] ∈ Σ_m. We assume that g(x, s) = γ(x, s)s + h(x, s) and the nonlinearity g satisfies ALP type condition. |
| Rights: | © World Scientific and Engineering Academy and Society |
| Appears in Collections: | Články / Articles (NTIS) Články / Articles (KMA) OBD |
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