Semilinear elliptic equations with near critical growth rates

DOI10.1017/S0308210500031140zbMath0662.35003MaRDI QIDQ3811004

Chris J. Budd

Publication date: 1987

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

symmetric solutionscritical Sobolev exponentnumerical calculationsperturbed Hamiltonian systemfold bifurcationasymptotic descriptionsemilinearMelnikov methods

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Bifurcations in context of PDEs (35B32)

Related Items (12)

Asymptotic behaviour of positive solutions of elliptic equations with critical and supercritical growth. I: The radial case ⋮ Elliptic equations with nearly critical growth ⋮ Comparison theorems for radial solutions of semilinear elliptic equations ⋮ Energy asymptotics in the three-dimensional Brezis-Nirenberg problem ⋮ A non-oscillation theorem for the Emden-Fowler equation: Ground states for semilinear elliptic equations with critical exponents ⋮ Adaptive methods for semi-linear elliptic equations with critical exponents and interior singularities ⋮ Symmetry breaking and semilinear elliptic equations ⋮ Asymptotic behaviour of positive solutions of elliptic equations with critical and supercritical growth. II: The nonradial case ⋮ A singularity theory approach to a semilinear boundary value problem ⋮ Large positive solutions of semilinear elliptic equations with critical and supercritical growth ⋮ Asymptotic behaviour of solutions of elliptic equations with critical exponents and Neumann boundary conditions ⋮ Singular ground states of semilinear elliptic equations via invariant manifold theory

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• An example of bifurcation to homoclinic orbits
• Semilinear elliptic equations and supercritical growth
• A note on integration of the Emden-Fowler equation
• On the positive of boundary-value problems for a class of nonlinear differential equations
• Some global results for nonlinear eigenvalue problems
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Uniqueness and nonuniqueness for positive radial solutions of Δu + f(u, r) = 0
• Emden-Fowler equations involving critical exponents
• The Calculation of Turning Points of Nonlinear Equations
• Uniqueness of solutions of nonlinear Dirichlet problems
• Perturbed bifurcation theory

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