Nonlinear second order elliptic partial differential equations at resonance

Iannacci, R.; Nkashama, M. N.; Ward, J. R.

doi:10.1090/S0002-9947-1989-0951886-3

Nonlinear second order elliptic partial differential equations at resonance
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by R. Iannacci, M. N. Nkashama and J. R. Ward PDF

Trans. Amer. Math. Soc. 311 (1989), 711-726 Request permission

Abstract:

In this paper we study the solvability of boundary value problems for semilinear second order elliptic partial differential equations of resonance type in which the nonlinear perturbation is not (necessarily) required to satisfy the Landesman-Lazer condition or the monotonicity assumption. The nonlinearity may be unbounded and some crossing of eigenvalues is allowed. Selfadjoint and nonselfadjoint resonance problems are considered.

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A note on the Dirichlet problem for some semi-linear elliptic equations