Bifurcation phenomena associated to the $p$-Laplace operator
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- by Mohammed Guedda and Laurent VĂ©ron PDF
- Trans. Amer. Math. Soc. 310 (1988), 419-431 Request permission
Abstract:
We determine the structure of the set of the solutions $u$ of $- {(|{u_x}{|^{p - 2}}{u_x})_x} + f(u) = \lambda |u{|^{p - 2}}u$ on $(0, 1)$ such that $u(0) = u(1) = 0$, where $p > 1$ and $\lambda \in {\mathbf {R}}$. We prove that the solutions with $k$ zeros are unique when $1 < p \leqslant 2$ but may not be so when $p > 2$.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 310 (1988), 419-431
- MSC: Primary 35B32; Secondary 35J60
- DOI: https://doi.org/10.1090/S0002-9947-1988-0965762-2
- MathSciNet review: 965762