General existence principles for nonlocal boundary value problems with φ-Laplacian and their applications
The paper presents general existence principles which can be used for a large class of nonlocal boundary value problems of the form (φ(x′))′=f1(t,x,x′)+f2(t,x,x′)F1x+f3(t,x,x′)F2x,α(x)=0, β(x)=0, where fj satisfy local Carathéodory conditions on some [0,T]×𝒟j⊂ℝ2, fj are either regular or...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA/2006/96826 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832566901272739840 |
|---|---|
| author | Ravi P. Agarwal Donal O'Regan Svatoslav Stanek |
| author_facet | Ravi P. Agarwal Donal O'Regan Svatoslav Stanek |
| author_sort | Ravi P. Agarwal |
| collection | DOAJ |
| description | The paper presents general existence principles which can be used
for a large class of nonlocal boundary value problems of the form (φ(x′))′=f1(t,x,x′)+f2(t,x,x′)F1x+f3(t,x,x′)F2x,α(x)=0, β(x)=0, where fj satisfy local Carathéodory
conditions on some [0,T]×𝒟j⊂ℝ2, fj are either regular or have singularities in their phase variables (j=1,2,3), Fi:C1[0,T]→C0[0,T](i=1,2), and α,β:C1[0,T]→ℝ are continuous. The proofs
are based on the Leray-Schauder degree theory and use
regularization and sequential techniques. Applications of general
existence principles to singular BVPs are given. |
| format | Article |
| id | doaj-art-6abe1c905f8e44b48c786e735faac8eb |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-6abe1c905f8e44b48c786e735faac8eb2025-02-03T01:02:47ZengWileyAbstract and Applied Analysis1085-33751687-04092006-01-01200610.1155/AAA/2006/9682696826General existence principles for nonlocal boundary value problems with φ-Laplacian and their applicationsRavi P. Agarwal0Donal O'Regan1Svatoslav Stanek2Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, Florida 32901-6975, USADepartment of Mathematics, National University of Ireland, Galway, IrelandDepartment of Mathematical Analysis, Faculty of Science, Palacký University, Tomkova 40, Olomouc 779 00, Czech RepublicThe paper presents general existence principles which can be used for a large class of nonlocal boundary value problems of the form (φ(x′))′=f1(t,x,x′)+f2(t,x,x′)F1x+f3(t,x,x′)F2x,α(x)=0, β(x)=0, where fj satisfy local Carathéodory conditions on some [0,T]×𝒟j⊂ℝ2, fj are either regular or have singularities in their phase variables (j=1,2,3), Fi:C1[0,T]→C0[0,T](i=1,2), and α,β:C1[0,T]→ℝ are continuous. The proofs are based on the Leray-Schauder degree theory and use regularization and sequential techniques. Applications of general existence principles to singular BVPs are given.http://dx.doi.org/10.1155/AAA/2006/96826 |
| spellingShingle | Ravi P. Agarwal Donal O'Regan Svatoslav Stanek General existence principles for nonlocal boundary value problems with φ-Laplacian and their applications Abstract and Applied Analysis |
| title | General existence principles for nonlocal boundary value problems with φ-Laplacian and their applications |
| title_full | General existence principles for nonlocal boundary value problems with φ-Laplacian and their applications |
| title_fullStr | General existence principles for nonlocal boundary value problems with φ-Laplacian and their applications |
| title_full_unstemmed | General existence principles for nonlocal boundary value problems with φ-Laplacian and their applications |
| title_short | General existence principles for nonlocal boundary value problems with φ-Laplacian and their applications |
| title_sort | general existence principles for nonlocal boundary value problems with φ laplacian and their applications |
| url | http://dx.doi.org/10.1155/AAA/2006/96826 |
| work_keys_str_mv | AT ravipagarwal generalexistenceprinciplesfornonlocalboundaryvalueproblemswithphlaplacianandtheirapplications AT donaloregan generalexistenceprinciplesfornonlocalboundaryvalueproblemswithphlaplacianandtheirapplications AT svatoslavstanek generalexistenceprinciplesfornonlocalboundaryvalueproblemswithphlaplacianandtheirapplications |