Non-resonant boundary value problems with singular {\phi} -Laplacian operators |
| |
Authors: | Cristian Bereanu Dana Gheorghe Manuel Zamora |
| |
Institution: | 1. Institute of Mathematics “Simion Stoilow”, Romanian Academy, Calea Grivi?ei 21, Sector 1, 010702, Bucharest, Romania 2. Military Technical Academy, Bld - George Cosbuc, No. 81-83, 050141, Bucharest, Romania 3. Departamento de Matemática Aplicada, Universidad de Granada, 18071, Granada, Spain
|
| |
Abstract: | In this paper, using Leray–Schauder degree arguments, critical point theory for lower semicontinuous functionals and the method of lower and upper solutions, we give existence results for periodic problems involving the relativistic operator ${u \mapsto \left(\frac{u^\prime}{\sqrt{1-u^\prime 2}}\right)^\prime+r(t)u}$ with ${\int_0^Tr dt\neq 0}$ . In particular we show that in this case we have non-resonance, that is periodic problem $$\left(\frac{u^\prime}{\sqrt{1-u^\prime 2}}\right)^\prime+r(t)u=e(t),\quad u(0)-u(T)=0=u^\prime(0)-u^\prime(T),$$ has at least one solution for any continuous function ${e : 0, T] \to \mathbb {R}}$ . Then, we consider Brillouin and Mathieu-Duffing type equations for which ${r(t) \equiv b_1 + b_2 {\rm cos} t {\rm and} b_1, b_2 \in \mathbb{R}}$ . |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|