Bifurcation of Gradient Mappings Possessing the Palais‐Smale Condition
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This paper considers bifurcation at the principal eigenvalue of a class of gradient operators which possess the Palais‐Smale condition. The existence of the bifurcation branch and the asymptotic nature of the bifurcation is verified by using the compactness in the Palais Smale condition and the order of the nonlinearity in the operator. The main result is applied to estimate the asyptotic behaviour of solutions to a class of semilinear elliptic equations with a critical Sobolev exponent.
Morse-Smale systems, Variational problems in abstract bifurcation theory in infinite-dimensional spaces, Local and nonlocal bifurcation theory for dynamical systems, bifurcation, QA1-939, eigenvalue, Palais-Smale condition, Ekeland variational principle, Mathematics
Morse-Smale systems, Variational problems in abstract bifurcation theory in infinite-dimensional spaces, Local and nonlocal bifurcation theory for dynamical systems, bifurcation, QA1-939, eigenvalue, Palais-Smale condition, Ekeland variational principle, Mathematics
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