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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA/2006/96826 |
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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |