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Displaying similar documents to “The Picone identity for a class of partial differential equations”

Picone’s identity for a Finsler p -Laplacian and comparison of nonlinear elliptic equations

Jaroslav Jaroš (2014)

Mathematica Bohemica

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In the paper we present an identity of the Picone type for a class of nonlinear differential operators of the second order involving an arbitrary norm H in ℝ n which is continuously differentiable for x ≠ 0 and such that H p is strictly convex for some p > 1 . Two important special cases are the p -Laplacian and the so-called pseudo p -Laplacian. The identity is then used to establish a variety of comparison results concerning nonlinear degenerate elliptic equations which involve such operators. We...

Qualitative theory of half-linear second order differential equations

Ondřej Došlý (2002)

Mathematica Bohemica

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Some recent results concerning properties of solutions of the half-linear second order differential equation ( r ( t ) Φ ( x ' ) ) ' + c ( t ) Φ ( x ) = 0 , Φ ( x ) : = | x | p - 2 x , p > 1 , ( * ) are presented. A particular attention is paid to the oscillation theory of ( * ) . Related problems are also discussed.