Petr Tomiczek, "Jumping Unbounded Nonlinearities and ALP Condition," WSEAS Transactions on Mathematics, vol. 21, pp. 196-206, 2022, DOI:10.37394/23206.2022.21.26
Petr Tomiczek. Jumping Unbounded Nonlinearities and ALP Condition.
WSEAS Transactions on Mathematics. 2022;21:196-206. 10.37394/23206.2022.21.26
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 21, 2022
Jumping Unbounded Nonlinearities and ALP Condition
Author:
Abstract: We investigate the existence of solutions to the nonlinear problem
$$u^{′′} (x) + λ_{+}u^{+}(x) − λ_{−}u^{ −} (x) + g(x, u(x)) = f(x) , x \in (0, 2π), u(0) = u(2π) , u^{′} (0) = u^{′} (2π), $$
where the point $$[λ_{+}, λ_{−}]$$ is a point of the Fučík spectrum $$\sum = \bigcup_{m=0}^{\infty}\sum m$$.We denote $$φ_{m}$$ any nontrivial solution to
our problem with $$g = f = 0$$ corresponding to $$λ_{+}, λ_{−} \in \sum m$$. We assume that $$g(x, s) = γ(x, s)s + h(x, s)$$ and
the nonlinearity g satisfies ALP type condition
Keywords:
Second order ODE, periodic, resonance, jumping nonlinearities, Dancer-Fucik spectrum, ALP
condition, saddle point theorem
Pages: 196-206 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 21, 2022, Art. #26 DOI: 10.37394/23206.2022.21.26
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