# WEAK SOLUTIONS FOR THE p-LAPLACIAN WITH A NONLINEAR BOUNDARY CONDITION AT RESONANCE

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A p-Laplacian boundary-value problem with positive nonlinearity is considered. The existence of a continuum of positive solutions emanating from (Î», u) = (0, 0) is shown, and it can be extended to Î» = âˆž. Under an additional condition on the nonlinearity, it is shown that the positive...

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- The Existence of Positive Solutions for Third-Order p-Laplacian m-Point Boundary Value Problems with Sign Changing Nonlinearity on Time Scales. Fuyi Xu; Zhaowei Meng // Advances in Difference Equations;2009, Special section p1
We study the following third-order p-Laplacian m-point boundary value problems on time scales (íœ™p (uâˆ†âˆ‡))âˆ‡ + a(t) f (t, u(t)) = 0, t âˆˆ [0,T] TK, u(0) = âˆ‘i=1m-2 biu(í›i, uâˆ† (T) = 0, íœ™p (uâˆ†âˆ‡ (0)) = âˆ‘i=1m-2 ciíœ™p...