2 results
A p(x)-Laplacian extension of the Díaz-Saa inequality and some applications
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 150 / Issue 1 / February 2020
- Published online by Cambridge University Press:
- 24 January 2019, pp. 205-232
- Print publication:
- February 2020
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The main result of this work is a new extension of the well-known inequality by Díaz and Saa which, in our case, involves an anisotropic operator, such as the p(x)-Laplacian,
$\Delta _{p(x)}u\equiv {\rm div}( \vert \nabla u \vert ^{p(x)-2}\nabla u)$. Our present extension of this inequality enables us to establish several new results on the uniqueness of solutions and comparison principles for some anisotropic quasilinear elliptic equations. Our proofs take advantage of certain convexity properties of the energy functional associated with the p(x)-Laplacian.
Some elliptic semilinear indefinite problems on RN
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 134 / Issue 2 / April 2004
- Published online by Cambridge University Press:
- 12 July 2007, pp. 333-361
- Print publication:
- April 2004
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This paper deals with the existence and the behaviour of global connected branches of positive solutions of the problem
The function f is allowed to change sign and has an asymptotically linear or a superlinear behaviour.
