Geodesic
On the Solvability of a Neumann Boundary Value Problem at Resonance
Canadian mathematical bulletin, Tome 40 (1997) no. 4, pp. 464-470

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DOI

We study the existence of solutions of the semilinear equations (1) in which the non-linearity g may grow superlinearly in u in one of directions u → ∞ and u → −∞, and (2) −Δu + g(x, u) = h, in which the nonlinear term g may grow superlinearly in u as |u| → ∞. The purpose of this paper is to obtain solvability theorems for (1) and (2) when the Landesman-Lazer condition does not hold. More precisely, we require that h may satisfy are arbitrarily nonnegative constants, . The proofs are based upon degree theoretic arguments.
DOI : 10.4153/CMB-1997-055-7
Mots-clés : 35J65, 47H11, 47H15, Landesman-Lazer condition, Leray Schauder degree 
Kuo, Chung-Cheng. On the Solvability of a Neumann Boundary Value Problem at Resonance. Canadian mathematical bulletin, Tome 40 (1997) no. 4, pp. 464-470. doi: 10.4153/CMB-1997-055-7
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     title = {On the {Solvability} of a {Neumann} {Boundary} {Value} {Problem} at {Resonance}},
     journal = {Canadian mathematical bulletin},
     pages = {464--470},
     year = {1997},
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     number = {4},
     doi = {10.4153/CMB-1997-055-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1997-055-7/}
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