Boundary value problems for quasilinear ODEs
SourceNonlinear Analysis, Theory, Methods and Applications
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A priori bounds for the quasilinear ordinary differential equations (ODE), are discussed. A priori bounds for the derivative of the solution of one-dimensional p-Laplacian are proved. The global solvability of quasilinear second ODE for p=2 is also described. A priori bounds for derivatives of solutions can also be obtained once the bounds are found for the solutions themselves, provided that the nonlinearity in f is at most quadratic in z.