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Existence principles for singular vector nonlocal boundary value problems with \(\phi\)-Laplacian and their applications. (English) Zbl 1258.34045
The paper establishes existence principles for the solutions of singular differential systems of \(\phi\)-Laplacian type \[ \phi(u')' = f(t,u,u') \] under nonlocal boundary conditions. The nonlinearity \(f\) may be singular in the state variables. Under appropriate growth conditions, an existence result is obtained via the regularization technique and the Leray-Schauder degree theory.

MSC:
34B16 Singular nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
47H11 Degree theory for nonlinear operators
47N20 Applications of operator theory to differential and integral equations
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