Generalized Pohozhaev’s identity for radial solutions of p-Laplace equations
-
Philip Korman
Abstract
We derive a generalized Pohozhaev’s identity for radial solutions of p-Laplace equations, by using the approach in [P. Korman, Global Solution Curves for Semilinear Elliptic Equations, World Scientific Publishing, Hackensack, 2012], thus extending the work [H. Brézis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 1983, 4, 437–477], where this identity was implicitly used for the Laplace equation.
Acknowledgements
It is a pleasure to thank Florin Catrina for a number of useful discussions.
References
[1] F. V. Atkinson, H. Brezis and L. A. Peletier, Nodal solutions of elliptic equations with critical Sobolev exponents, J. Differential Equations 85 (1990), no. 1, 151–170. 10.1016/0022-0396(90)90093-5Search in Google Scholar
[2] H. Brézis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), no. 4, 437–477. 10.1002/cpa.3160360405Search in Google Scholar
[3] C. Budd and J. Norbury, Semilinear elliptic equations and supercritical growth, J. Differential Equations 68 (1987), no. 2, 169–197. 10.1016/0022-0396(87)90190-2Search in Google Scholar
[4] F. Catrina, A refinement of the radial Pohozaev identity, Math. Bohem. 135 (2010), no. 2, 143–150. 10.21136/MB.2010.140691Search in Google Scholar
[5] P. Korman, Global Solution Curves for Semilinear Elliptic Equations, World Scientific Publishing, Hackensack, 2012. 10.1142/8308Search in Google Scholar
[6] P. Korman, Non-existence of solutions for non-autonomous elliptic systems of Hamiltonian type, Comm. Appl. Nonlinear Anal. 21 (2014), no. 3, 13–20. Search in Google Scholar
[7] P. Korman and D. S. Schmidt, Continuation of global solution curves using global parameters, preprint (2020), https://arxiv.org/abs/2001.00616. Search in Google Scholar
[8]
P. Korman and D. S. Schmidt,
Solving partial differential equations on balls in
[9] M. K. Kwong and Y. Li, Uniqueness of radial solutions of semilinear elliptic equations, Trans. Amer. Math. Soc. 333 (1992), no. 1, 339–363. 10.1090/S0002-9947-1992-1088021-XSearch in Google Scholar
[10]
L. A. Peletier and J. Serrin,
Uniqueness of nonnegative solutions of semilinear equations in
[11] K. Schmitt, Positive solutions of semilinear elliptic boundary value problems, Topological Methods in Differential Equations and Inclusions (Montreal 1994), NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 472, Kluwer Academic Publishers, Dordrecht (1995), 447–500. 10.1007/978-94-011-0339-8_10Search in Google Scholar
© 2022 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- B-essential spectra of 2 × 2 block operator matrix pencils
- New results on perturbations of p-adic linear operators
- Approximation by matrix transform means with respect to the character system of the group of 2-adic integers
- Pentactions and action representability in the category of reduced groups with action
- On interpolation of reflexive variable Lebesgue spaces on which the Hardy–Littlewood maximal operator is bounded
- Further inequalities for the 𝔸-numerical radius of certain 2 × 2 operator matrices
- A generalization of practical stability of nonlinear impulsive systems
- Properties of rational Fourier series and generalized Wiener class
- Some identities on degenerate hyperharmonic numbers
- Generalized Pohozhaev’s identity for radial solutions of p-Laplace equations
- Classes of trivial ring extensions and amalgamations subject to pseudo-almost valuation condition
- Anisotropic nonlinear weighted elliptic equations with variable exponents
- Finite groups in which every non-nilpotent subgroup is a TI-subgroup or has p;'-order
- Finite-time attractivity of strong solutions for generalized nonlinear abstract Rayleigh–Stokes equations
- Reproducing kernels and minimal solutions of elliptic equations
Articles in the same Issue
- Frontmatter
- B-essential spectra of 2 × 2 block operator matrix pencils
- New results on perturbations of p-adic linear operators
- Approximation by matrix transform means with respect to the character system of the group of 2-adic integers
- Pentactions and action representability in the category of reduced groups with action
- On interpolation of reflexive variable Lebesgue spaces on which the Hardy–Littlewood maximal operator is bounded
- Further inequalities for the 𝔸-numerical radius of certain 2 × 2 operator matrices
- A generalization of practical stability of nonlinear impulsive systems
- Properties of rational Fourier series and generalized Wiener class
- Some identities on degenerate hyperharmonic numbers
- Generalized Pohozhaev’s identity for radial solutions of p-Laplace equations
- Classes of trivial ring extensions and amalgamations subject to pseudo-almost valuation condition
- Anisotropic nonlinear weighted elliptic equations with variable exponents
- Finite groups in which every non-nilpotent subgroup is a TI-subgroup or has p;'-order
- Finite-time attractivity of strong solutions for generalized nonlinear abstract Rayleigh–Stokes equations
- Reproducing kernels and minimal solutions of elliptic equations
