Nontrivial solutions of a semilinear elliptic problem via variational methods

DOI10.1017/S0004972700036005zbMath1097.35057MaRDI QIDQ4824813

Zhi-Qing Han

Publication date: 1 November 2004

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Mathematics Subject Classification ID

Variational inequalities (49J40) Nonlinear boundary value problems for linear elliptic equations (35J65) Existence of solutions for minimax problems (49J35) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05)

Related Items (4)

Computations of critical groups and applications to some differential equations at resonance ⋮ Nontrivial solutions to non-local problems with sublinear or superlinear nonlinearities ⋮ Periodic solutions to second order nonautonomous differential systems with gyroscopic forces ⋮ Existence of critical point for abstract resonant problems with unbounded nonlinearities and applications to differential equations

Cites Work

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• Nonresonance below the first eigenvalue for a semilinear elliptic problem
• Elliptic resonant problems at higher eigenvalues with an unbounded nonlinear term
• The computations of the critical groups with an application to elliptic resonant problems at a higher eigenvalue
• Asymptotically linear elliptic equations without nonresonance conditions
• Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity
• On the Dirichlet problem for weakly non-linear elliptic partial differential equations
• Existence of nontrivial solutions of semilinear elliptic equations
• On the existence of a nontrivial solution to nonlinear problems at resonance

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