Ambrosetti–Prodi Type Results for Dirichlet Problems of Fractional Laplacian-Like Operators
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DOI: 10.1007/s00020-020-02584-7
Abstract: We establish Ambrosetti–Prodi type results for viscosity and classical solutions of nonlinear Dirichlet problems for fractional Laplace and comparable operators. In the choice of nonlinearities we consider semi-linear and super-linear growth cases separately. We develop… read more here.
Keywords: ambrosetti prodi; prodi type; problems fractional; results dirichlet ... See more keywords
Some cases of weak continuity in nonlinear Dirichlet problems
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Functional Analysis"
DOI: 10.1016/j.jfa.2019.05.020
Abstract: Abstract We show how to pass to the limit in some nonlinear elliptic problems, despite the weak convergence of the right hand sides (and the weak convergence of the solutions). read more here.
Keywords: cases weak; continuity nonlinear; dirichlet problems; weak continuity ... See more keywords
Nonlinear Dirichlet problems with unilateral growth on the reaction
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DOI: 10.1515/forum-2018-0114
Abstract: Abstract We consider a nonlinear Dirichlet problem driven by the p-Laplace differential operator with a reaction which has a subcritical growth restriction only from above. We prove two multiplicity theorems producing three nontrivial solutions, two… read more here.
Keywords: nonlinear dirichlet; dirichlet; problems unilateral; reaction ... See more keywords
Stability of Non-Linear Dirichlet Problems with ϕ-Laplacian
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DOI: 10.3390/e23060647
Abstract: We study the stability and the solvability of a family of problems −(ϕ(x′))′=g(t,x,x′,u)+f* with Dirichlet boundary conditions, where ϕ, u, f* are allowed to vary as well. Applications for boundary value problems involving the p-Laplacian… read more here.
Keywords: problems laplacian; stability non; non linear; linear dirichlet ... See more keywords
Dirichlet problems for second order linear elliptic equations with $ L^{1} $-data
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DOI: 10.3934/cpaa.2023051
Abstract: We consider the Dirichlet problems for second order linear elliptic equations in non-divergence and divergence forms on a bounded domain $\Omega$ in $\mathbb{R}^n$, $n \ge 2$: $$ -\sum_{i,j=1}^n a^{ij}D_{ij} u + b \cdot D u… read more here.
Keywords: linear elliptic; elliptic equations; order linear; dirichlet problems ... See more keywords