Some general existence principles and results for fy′ =qft,y,y′ ,0
SIAM Journal on Mathematical Analysis
Time-mappings and multiplicity of solutions for the one-dimensional p-Laplacian
Nonlinear Analysis: Theory, Methods & Applications
Pairs of positive solutions for the one-dimensional p-Laplacian
Nonlinear Analysis: Theory, Methods & Applications
Existence results for the problem (&phgr;(u′))′ = f(t, u, u′) with nonlinear boundry conditions
Nonlinear Analysis: Theory, Methods & Applications
Nonlinear Analysis: Theory, Methods & Applications
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In this paper we consider the solvability of equations of the form -d/dt φ(t, u, u(t), u'(t)) = f(t, u, u(t), u'(t)) for a.e. t ∈ I = [a,b] subject to a general type of functional-boundary conditions which cover Dirichlet and periodic boundary data as particular cases. Our approach is that of upper and lower solutions together with growth restrictions of Nagumo's type. An example is provided where a p-Laplacian with variable p is shown to have a solution between given upper and lower solutions.