Existence results for nonlinear boundary value problems under nonresonance conditions

We give applications of Banach, Schauder, Darbo and Leray-Schauder fixed point theorems to prove existence results for weak solutions of the semilinear Dirichlet problem -△u cu -f(x,u)▽u) in Ω,u=0 on ∂u, under the assupmtion that c is not an eigenvalue of -△ and f(x,u,v) has linear growth on u and v.We obtain improvements of some known existence results.

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We give applications of Banach, Schauder, Darbo and Leray-Schauder fixed point
theorems to prove existence results for weak solutions of the semilinear
Dirichlet problem\(-\triangle u-cu-f(x,u)\triangledown u)\ \) in \(\
\Omega, u=0\) on \(\partial u\), under the assupmtion that \(c\) is not an eigenvalue of
\(-\triangle\\) and \(\ f(x,u,v)\) has linear growth on \(u\) and \(v\).We obtain
improvements of some known existence results.

Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

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R. Precup, Existence results for nonlinear boundary value problems under nonresonance conditions, In: “Qualitative Problems for Differential Equations and Control Theory”, C. Corduneanu ed., World Sci. Publishing, River Edge, 1995, 263-273

https://ictp.acad.ro/wp-content/uploads/2023/03/1995A-Precup-Existence-results-for-nonlinear-boundary-value-problems-under-nonresonance-conditions.pdf

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MR: 96j:35083