Existence and multiplicity of solutions for non-degenerate Kirchhoff type problem with nonlinear boundary condition
We show the existence of solutions for nonlinear elliptic partial differential equations with Steklov nonlinear boundary conditions involving a Kirchhoff type operator. By using variational and topological methods, we prove the existence and multiplicity of solutions. The results obtained are...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Texas State University
2019-03-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2019/42/abstr.html |
| _version_ | 1818017799443841024 |
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| author | Mateus Balbino Guimaraes Elard Juarez Hurtado Rodrigo da Silva Rodrigues |
| author_facet | Mateus Balbino Guimaraes Elard Juarez Hurtado Rodrigo da Silva Rodrigues |
| author_sort | Mateus Balbino Guimaraes |
| collection | DOAJ |
| description | We show the existence of solutions for nonlinear elliptic partial differential
equations with Steklov nonlinear boundary conditions involving a Kirchhoff
type operator. By using variational and topological methods, we prove the
existence and multiplicity of solutions. The results obtained are new even
for the standard stationary Kirchhoff equation with nonlinear
boundary condition involving the p-Laplacian operator. |
| first_indexed | 2024-04-14T07:31:31Z |
| format | Article |
| id | doaj.art-edbc6bca11c04e92bb8c1cbebb5990a4 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-14T07:31:31Z |
| publishDate | 2019-03-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-edbc6bca11c04e92bb8c1cbebb5990a42022-12-22T02:05:51ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912019-03-01201942,112Existence and multiplicity of solutions for non-degenerate Kirchhoff type problem with nonlinear boundary conditionMateus Balbino Guimaraes0Elard Juarez Hurtado1Rodrigo da Silva Rodrigues2 Inst. Federal do Sudeste de Minas Gerais, Brazil Univ. Estadual Paulista, Brazil Univ. Federal de Sao Carlos, Brazil We show the existence of solutions for nonlinear elliptic partial differential equations with Steklov nonlinear boundary conditions involving a Kirchhoff type operator. By using variational and topological methods, we prove the existence and multiplicity of solutions. The results obtained are new even for the standard stationary Kirchhoff equation with nonlinear boundary condition involving the p-Laplacian operator.http://ejde.math.txstate.edu/Volumes/2019/42/abstr.htmlVariational methodsnonlinear elliptic equationsSteklov-Neumann eigenvalues |
| spellingShingle | Mateus Balbino Guimaraes Elard Juarez Hurtado Rodrigo da Silva Rodrigues Existence and multiplicity of solutions for non-degenerate Kirchhoff type problem with nonlinear boundary condition Electronic Journal of Differential Equations Variational methods nonlinear elliptic equations Steklov-Neumann eigenvalues |
| title | Existence and multiplicity of solutions for non-degenerate Kirchhoff type problem with nonlinear boundary condition |
| title_full | Existence and multiplicity of solutions for non-degenerate Kirchhoff type problem with nonlinear boundary condition |
| title_fullStr | Existence and multiplicity of solutions for non-degenerate Kirchhoff type problem with nonlinear boundary condition |
| title_full_unstemmed | Existence and multiplicity of solutions for non-degenerate Kirchhoff type problem with nonlinear boundary condition |
| title_short | Existence and multiplicity of solutions for non-degenerate Kirchhoff type problem with nonlinear boundary condition |
| title_sort | existence and multiplicity of solutions for non degenerate kirchhoff type problem with nonlinear boundary condition |
| topic | Variational methods nonlinear elliptic equations Steklov-Neumann eigenvalues |
| url | http://ejde.math.txstate.edu/Volumes/2019/42/abstr.html |
| work_keys_str_mv | AT mateusbalbinoguimaraes existenceandmultiplicityofsolutionsfornondegeneratekirchhofftypeproblemwithnonlinearboundarycondition AT elardjuarezhurtado existenceandmultiplicityofsolutionsfornondegeneratekirchhofftypeproblemwithnonlinearboundarycondition AT rodrigodasilvarodrigues existenceandmultiplicityofsolutionsfornondegeneratekirchhofftypeproblemwithnonlinearboundarycondition |