Boundary value problems for strongly nonlinear equations under a Wintner-Nagumo growth condition
2017
We study the following strongly nonlinear differential equation:
$$\bigl(a \bigl(t,x(t) \bigr)\Phi\bigl(x'(t) \bigr) \bigr)'= f \bigl(t,x(t),x'(t) \bigr), \quad\text{a.e. in } [0,T] $$
subjected to various boundary conditions including, as particular cases, the classical Dirichlet, periodic, Neumann and Sturm-Liouville problems. We adopt the method of lower and upper solutions requiring a weak form of a Wintner-Nagumo growth condition.
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