On the dependence on parameters for mountain pass solutions of second-order discrete BVP's (Q371566)
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scientific article; zbMATH DE number 6214596
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the dependence on parameters for mountain pass solutions of second-order discrete BVP's |
scientific article; zbMATH DE number 6214596 |
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On the dependence on parameters for mountain pass solutions of second-order discrete BVP's (English)
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10 October 2013
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discrete \(p\)-Laplacian
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mountain pass solution
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dependence on parameters
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nontrivial solution
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boundary value problem
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half linear difference equation
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The authors consider the boundary value problem for the half linear difference equation NEWLINE\[NEWLINE -\Delta(\phi_p(\Delta u(k-1))) = f(k,u(k),w)\;,\;k=\overline{1,T}\;;\;u(0)= u(T)=0, NEWLINE\]NEWLINE where \(\phi_p(t)=|t|^{p-2}t\), \(\Delta u(k)=u(k+1)-u(k)\), \(w\in W\), with \(W\) some linear topological space.NEWLINENEWLINEUnder a set of basic assumptions the solutions are considered in the variational settings, in the context of the mountain pass lemma. It is shown that the existence of nontrivial solutions implies Hadamard well posedness.
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